What is a factor of 100? exactly how do I find them? Is a divisor various from a factor?

All of these inquiries will be answered in this lesson.

You are watching: Which number is a factor of 100?

**A element is a number that divides, or walk into, one more number exactly.**

Another method of speak this is that the other number is a many of the factor.

In a same world, sharing 12 coco bars in between 4 world leaves each person with 3 chocolate bars.

In this case: **3 and 4 are determinants of 12** because they can each divide 12 without any kind of remainders – no leftover chunks of chocolate!

**IMPORTANT:**

Divisor is **another word** for factor. Both words will be supplied interchangeably v this lesson therefore you can get an ext comfortable through them.

Contents

100’s factors Pairs Primes how to discover 100’s factors Divisibility Tests element Factoriziation the 100 Isn’t 100 Interesting? 100 is a really Imporant Number Why is 100 Everywhere? To sum Up (Pun Intended!)

## All the factors of 100

The determinants of 100 room **1, 2, 4, 5, 10, 20, 25, 50, and also 100**.

If you want a fast reference, look at this useful table of the determinants of 1 come 100, consisting of primes, and the first 20 multiples.

Otherwise, review on and also conquer the factor!

### Factor pairs of 100

The pairs for 100 room each do from two entirety numbers, or **integers**, that multiply together to make 100.

Since they’re integers, they have the right to be confident or negative. Below they space in their pairs:

Positive PairNegative Pair(1, 100) | (-1, -100) |

(2, 50) | (-2, -50) |

(4, 25) | (-4, -25) |

(5, 20) | (-5, -20) |

(10, 10) | (-10, -10) |

It doesn’t matter which bespeak the multiplication number pairs are provided in, due to the fact that multiplication is commutative.

**Commutative** way number order can be swapped without making a distinction to the answer.

Both

4 × 25 = 100

and

25 × 4 = 100

are equal to 100.

So aspect pairs can be composed either means round prefer this **(4, 25)** or choose this **(25, 4)**.

They room both the very same pair.

We’ll have a look at at just how we uncovered these pairs later on.

### Prime components of 100

A element number can be divided only through 1 and itself.

EXAMPLE3 cannot be separated by an additional number apart from itself.

(3 ÷ 3 = 1)

and

(3 ÷ 1 = 3)

Its only components are 1 and also 3, so the is a element number.

So from a number’s divisors, at least one should be a prime.

For now, 100’s positive components are **1, 2, 4, 5, 10, 25, 50, and also 100**

Of these numbers, *only 2 and 5 space prime*, for this reason those space our element factors.

## How to discover the components of 100

If girlfriend would fairly read 보다 watch, proceed here.

A sensible means to discover the factors of any type of number is to uncover the pairs, by starting with 1, 2, 3, etc., and checking if they division the number the we want to factorize.

This way that as soon as we uncover one divisor, we deserve to divide ours number by it – which finds an additional divisor!

That’s how you make a pair.

Remember…

All factors, apart from square roots, come in pairs prefer this. For a square number, when splitting it by its square root, we gain the exact same number. For instance **100 ÷ 10 = 10**.

Fortunately, there room some tricks that enable us to quickly inspect whether a number is divisible through another.

They’re dubbed divisibility tests.

The table below shows some advantageous divisibility tests for the numbers 1 come 10, plenty of of i m sorry you’ll currently know, and also whether they offer a positive result applied to 100.

### Divisibility Tests as much as 10

Click the documents listed below for free, printable PDFs.

The an initial shows clearly the divisibility rules as much as 15 in a succinct table, great for checking your an approach as you go:

The second has 14 practice questions v answers, one inquiry for each divisibility dominance from 2 to 15:

Whether you usage the worksheets above or not, below are the handy hints for checking if 100 can be separated by number from 1 to 10.

Divisible by …?TestWorks for 100?1 | No test required – all numbers are divisible by 1 | ✅ |

2 | Even – number ends in 2, 4, 6, 8, or 0 | ✅ |

3 | Sum of digits is a multiple of 3 | ❌ |

4 | The number made by the critical 2 digits are divisible through 4 | ✅ |

5 | Number end in 0 or 5 | ✅ |

6 | Divisible through 2 and also 3 | ❌ |

7 | No basic test! | ❌ |

8 | Divisible by 4 after gift halved | ❌ |

9 | Sum of digits is a multiple of 9 | ❌ |

10 | Number end in 0 | ✅ |

Check i beg your pardon ones occupational for 100 to obtain the smaller sized factors: 1, 2, 4, 5, and also 10. Then divide 100 by each of this numbers – you’ll uncover the larger, matching component of the pair: 100, 50, 25, and 20.

This is a general an approach that functions for all numbers, but for the little numbers, you need to check all the means up come the square root of your number.

Coming up you will see, over there *is* a test for divisibility by 7, however it’s not rather as immediate as few of the others.

### Divisibility Test because that 7

It is still useful to know, therefore here’s how it works.

Divisibility Test for 7Subtract twice the last digit indigenous the remainder of the numberContinue until the number is much less than 70 or straightforward to divide by 7If the an outcome is divisible by 7, then so to be the original

Here’s one example. See if you deserve to work out the answers prior to expanding the boxes come check!

Is 392 divisible by 7? (Open for solution)392 ⟶ 39 – (2 × 2) = 35 = 7 × 5

So 392 is divisible by 7.

Okay, how about a much bigger number?

What about 6,608? (Open for solution)usage the same an approach as above, just apply it a few times.

6608 ⟶ 660 -8 × 2 = 644 644 ⟶ 64 -4 × 2 = 56 = 8 × 7

So 6,608 is likewise divisible through 7.

We’re fortunate that the square source of 100 is 10 because, for numbers bigger than 10, it it s okay a little trickier come test for divisibility.

identify if a number is divisible by 11:Start v the digit on the leftSubtract the digit to that is rightThen include the one ~ thatThen subtract the one ~ thatAnd for this reason onIf the resulting amount is a multiple of 11, climate so is the initial number.

Is 8195 divisible by eleven? (Open because that solution)

begin by adhering to 11’s divisibility rule, for this reason alternately individually and including one digit to the next, starting from the right.

8195 ⟶ 8, 1, 9, 5 8 – 1 + 9 – 5 = 11 = 1 × 11

So 8195 is a multiple of 11.

What about 5432? (Open for solution)

5432 ⟶ 5, 4, 3, 2 5 – 4 + 3 – 2 = 2

2 is no divisible by 11, for this reason 5432 is not a multiple of 11.

here’s a test for divisibility through 13:

Add 4 time the last digit to the staying digitsIf the an outcome is divisible by 13, then the initial number is too

You can use this process repeatedly to address larger numbers.

For example, let’s view if 2717 is divisible through 13:

2717 ⟶ 271 + 7 × 4 = 299

299 ⟶ 29 + 9 × 4 = 65 = 13 × 5

So, 2717 is divisible by 13.

What about 3049? (Open because that solution)3049 ⟶ 304 + (9 × 4) = 340

Have a go finding your very own divisibility tests because that 12, 14, and also 15. Climate you inspect for divisibility all the means up to 15!

Hint: They are not complex – look in ~ the test for 6 and also 8 for some ideas. Let us know what you come up through – comment below!

### Prime factorization of 100

Returning come the idea native earlier, there is a unique way of creating 100 together a product of just its prime factors. This is called its **prime factorization** or **prime decomposition**.

100 can be split into any type of two the its divisors, then each of those numbers have the right to be break-up up again right into two more. This is recurring until you’re only left with primes which us can’t separation up any type of further.

What you end up through is a **factor tree**, i m sorry looks favor this:

This tree is presented by the equation:

100 = 2 × 2 × 5 × 5 =22 × 52

So, the primes that divide 100 are 2 and also 5, and 100 has the **unique** prime factorization 22 × 52.

All integers have actually the special residential or commercial property that their prime decomposition is distinctive – yes no other method to make 100 using just prime numbers!

We can use the prime decomposition of a number to discover all that is divisors.

Since any kind of divisor of 100 is comprised of few of its prime factors, we simply remove some and also see what we’re left with:

2 = 2 4 = 2 × 2 5 = 5 10 = 2 × 5 20 = 2 × 2 × 5 25 = 5 × 5 50 = 2 × 5 × 5 100 = 2 × 2 × 5 × 5

What if you nothing care around what the divisors are, just how many there are?

There are 9 various divisors the 100, consisting of 1 and 100.

Remember…

How countless factors space there because that 1000?using the determinants of 100 together an example, have another look in ~ its element decomposition:

22 × 52

The variety of times every prime appears can’t be more than that power. There have the right to be no much more than two 5’s or two 2’s in any divisor the 100.

But are you permitted to have actually zero the a specific prime? The price is yes, so for each prime divisor, you have 3 selections for how plenty of times the is used: 0, 1, or 2 times.

Since there are two primes because that 100, you have actually **32 = 3 × 3 = 9** options in total.

Now for 1000. Have a go at making use of the factor tree method above because that finding the prime factorization.

You should obtain **1000 = 23 × 53**.

This way there space 4 choices of how many times every prime appears: 0, 1, 2, or 3 times. Usage this fact to show that 1000 has

4 × 4 = 16

factors in total.

CHALLENGE: How numerous factors go 1500 have? (Open for solution)

for 1500, the prime factorization is

22 × 3 × 53

Meaning over there are:

3 selections for the number of 2’s2 selections for the number of 3’s4 choices for the variety of 5’sThe number of choices is the exponent + 1 to encompass zero as an option.

Multiplying the variety of options together provides the number of possible combinations, therefore the number of divisors is:

3 × 2 × 4 = 24

There space 24 factors of 1500.

When you’ve finished v that, choose your favourite number and shot to discover its element factorization. Then, check out if you have the right to work out how plenty of factors that has!

And now that you know how to find prime factors, to save you time you deserve to use a tool prefer this to find them because that you.

## Isn’t 100 Interesting?

### 100 is a an extremely Important Number

100 cents in one dollar, 100 percent makes a whole, water boils in ~ 100°C conversely, 100°F is around human human body temperature.

100 year in a century, the typical adult IQ is 100, and there room 100 senators in the Senate.

100 even crops up in football: the ar is 100 yards long!

### Why is 100 Everywhere?

Simply, due to the fact that it’s a really ‘round’ number: 100 is 102, and also because most of the world’s number systems use basic 10 – the worth of 102 is really easy to transaction with.

However, the word ‘hundred’ wasn’t always used in this way…

Originally, ‘hundred’ supposed 120!

It to be a unit that measurement used in taxes in middle ages England, and also various countries in Europe.

But, depending on what to be being to buy or sold, because that some points ’hundred’ intended 120…

…for others, it expected 100 – how confusing!

exciting factbase 10 isn’t the only method that numbers can be viewed. Computers address binary (base 2) and also hexadecimal (base 16), wherein 100 isn’t practically as nice: in binary the is 1100100, and also in hexadecimal, it is 64.

Can you find various representations the 100 in other bases? Share her answer(s) in the comments below!

### 100 is incredibly Mathematically interesting Too!

It is the amount of the first 9 prime numbers:

100 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23

It is likewise the amount of the an initial 4 cubes, and the square the the amount from 1 come 4:

100 = 13 + 23 + 33 + 43 = (1 + 2 + 3 + 4)2

The right-angled triangle listed below has integer-length sides, with one of length 100:

We speak to these integer solutions to Pythagoras’ organize Pythagorean triples.

1002 + 6122 = 6292

Can friend find any type of other Pythagorean triples entailing the number 100?

Not only is 100 a square number, but it’s also an plentiful number.

A number is referred to as **abundant** if the sum of its components is better than twice the number itself.

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In the instance of 100, the full of it’s divisors is:

1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 100 = 217

It is clear to watch that

217 > 100×2

So 100 *is* an numerous number.

### What’s the Smallest plentiful Number?

Since the just divisors of a element number room 1 and also itself, if *p* is a prime, then the sum of its components is 1 + *p* *x*

2*x*

Sum the Factors

>2*x* ?

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