According come Aristotle, 56 is the number of layers the the Universe. He organized that planet is the an initial layer, with 55 crystalline spheres over it.

You are watching: What are the factor pairs of 56

This lesson will walk you through all 56’s factors, how to find the factors and also other interesting factor facts!

If you desire a rapid reference because that factors, this factors and multiples table will be much more useful.

A factor is a number that goes into one more number perfectly. Because that example, 2 is a factor of 10 since it goes into 10 perfectly without leaving a remainder.

If you multiply 2 by 5, you obtain 10, which means both 2 and also 5 are components of 10.

You will find out what 56’s components are, exactly how to discover factor pairs and also all around prime administer in this lesson.

Once you know this, girlfriend will have the ability to find the factors of any kind of number!

Contents

56’s determinants Pairs Primes Factorizing 56 exactly how to discover 56’s components Prime Factorization no 56 Interesting? To amount Up (Pun Intended!)

## All the components of 56 The determinants of 56 are 1, 2, 4, 7, 8, 14, 28, and also 56.

56 can be split by itself and also one, but it is also divisible by other numbers, so it is a composite number, and there are more than 2 factors!

As you have just learned, a factor is one number that divides one more without leaving a remainder.

You deserve to write a number in terms of its variable pairs or a product of its prime factors.

### Factor pairs of 56

The simplest way to discover all the determinants of a number is to work-related out the variable pairs.

Factor pairs room sets of two numbers the multiply together to make one more number.

So you need to find out which two numbers, X and also Y multiply together to make 56. This is composed as:

(X, Y)
aspect Pairs the 56
(1, 56) (2, 28) (4, 14) (7, 8)

Sometimes you have the right to include an adverse numbers together a factor because when two an adverse numbers room multiplied together, they make a confident number!

It is essential to remember the both numbers have to be negative to make a confident number. If one of them is negative, and one of lock is positive, they will certainly be negative.

an unfavorable Factor Pairs
(-1, -56) (-2, -28) (-4, -14) (-7, -8)

You have actually probably noticed the the an adverse factors room the same as the positive ones, only they’re negative!

However, only the confident ones are being referred to unless said otherwise as soon as talking around the element pairs.

### Is 56 Abundant?

If the amount of the positive components is bigger 보다 twice the number itself, the is known as an abundant number.

The amount of the positive determinants is:

120 = 1+2+4+7+8+14+28+56

Double 56 is 112, and the amount of all its determinants is 120. This makes 56 an abundant number: the amount of its factors is higher than double itself.

### Prime factors of 56

A prime number is one that cannot be divided by anything various other than 1 or itself. Because that example, 3.

3 ÷ 1 = 3 3 ÷ 3 = 1

3 can not be divided by anything else so it is a element number.

56 has actually only 2 prime factors, which are 2 and 7.

You deserve to use this prime factors to compose 56 as a product of its element factors.

56=2 × 2 × 2 × 7

You have the right to work this out by using any two factor pairs and also keep dividing them down till you have actually prime numbers.

This is a factor tree. It starts v the original number at the top, i m sorry is damaged down into variable pairs.

When a element is found, the is circled and the other number is damaged down further.

The prime number, 2, shows up on three occasions, for this reason this have the right to be written more simply utilizing power or exponent form.

56 = 23 × 7

The number 56 likewise has other prime numbers. You have the right to express 56 as the amount of continually primes.

56 = 3 + 5 + 7 + 11 + 13 + 17
Why uncover the prime Factors?

Finding all the prime components of a number can be helpful in finding the Greatest common Factor (GCF) of 2 numbers, and the Least usual Multiple (LCM) of two numbers.

Prime administrate is likewise useful in the real civilization in cryptography. It deserve to take an exceptionally long time to find a large number’s prime factorization, also for computers!

## Factorizing 56

### How to discover the components of 56

To uncover all the factors, you must start through 1 and work through each number one by one to 56, check if there is a remainder as soon as 56 is divided by each number. If over there is no remainder, the number is a factor.

Each time you uncover a element pair, you alleviate the expression of determinants you are trying to find to numbers in ~ such element pair intervals.

We will share a couple of tricks through you to do this a fast job.

The Process

starting at 1…

56 ÷ 1 = 56

There is no remainder, so friend have confirmed 1 and also 56 space a element pair. Girlfriend now need to uncover factors in between 1 and also 56.

56 ÷ 2 = 28

So, 2 and also 28 are a aspect pair. Girlfriend now need to find factors between 2 and also 28.

56 ÷ 3 = 18.67

So, 3 is no a factor. Proceed with this procedure with 4, 5, and also 6.

You will watch there space no determinants up come 6.

56 ÷ 7 = 56

7 and 8 are a factor pair. There are no integers in between 7 and 8, so friend have uncovered all the aspect pairs of 56.

So, in complete you have the complying with factors:

1, 2, 7, 8, 14, 28, 56

Here space a couple of tricks because that spotting factors:

All integers have a variable of 1Any even number has actually a variable of 2If the sum of the digits of a number is a multiple of 3 climate 3 is a factorNumbers with a factor of 4 should be even and if the last two digits are 00 or divisible by 4 then 4 is a factorAny number v the last digit 0 or 5 has actually a aspect of 5Any number that is even and the amount of that is digits room a multiple of 3 will have a variable of 6There no a basic trick because that spotting components of 7!If the critical 3 digits of a number room divisible through 8 that will have actually a element of 8If the amount of a number’s digits is a many of 9 then it has actually a aspect of 9Numbers with the last digit 0 will have actually a aspect of 10

These room so beneficial in fact, that we made a printable table the the divisibility rule from 2 to 15, add to a worksheet to practice, because that you to store with you–for your very own use. Simply click or insanity the images below!  Now, some practice.

using the an approach above, find the determinants of: a) 24 b) 37 c) 72 (Open to show solutions)

a) 1, 2, 3, 4, 6, 8, 12, 24

b) 37 is a element number, therefore the only determinants are 1, 37

c) 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

### Prime Factorization

Prime administer is finding all the element numbers i m sorry multiply together to do the original number.

The easiest an approach to discover all the prime numbers is to use a prime aspect tree.

At the start of the tree, you have actually 56.

Begin by picking two factor pairs the multiply together to do the number.

Choose the aspect pair through the the smallest prime number in it, e.g., 2 and 28, and include them together branches to the tree.

As 2 is a element number, you deserve to circle it to show it is the final factor on this branch, and it can not be separated anymore.

Now you require to continue breaking under 28 into its determinants by finding the smallest prime number the divides 28.

It is divisible through 2 again, so…

Again 2 deserve to be circled. Friend still need to malfunction 14, which, together it transforms out, is divisible by 2 again!

Both 2 and 7 room prime numbers, therefore you deserve to circle both.

Just prefer the variable tree girlfriend were displayed before, the end of every branch is circled, therefore you have completed your very own prime factor tree!

You have the right to now to express 56 as a product the the circled element factors.

56 = 2 × 2 × 2 × 7

This deserve to be neatened up by utilizing the strength or exponent form:

56 = 23 × 7
write each number as a product of its element factors. A) 48 b) 90 c) 104 (Open to present solutions)

a) 2×2×2×2×3=24×3

b) 2×3×3×5=2×32×5

c) 2×2×2×13=23×13

## Isn’t 56 Interesting?

There room several methods of to express 56, other than its factors, as it has some amazing properties.

56 is the amount of the an initial 6 triangular numbers.

56 = 1+3+6+10+15+21

A triangle number counts objects arranged in an it is provided triangle.

This renders 56 the 6th tetrahedral number as it is the sum of the an initial 6 triangle numbers, making it a triangle pyramidal number.

You can likewise express 56 as the amount of consecutive also or odd numbers.

For even numbers…

56 = 2+4+6+8+10+12+14

For odd numbers…

56 = 11+13+15+17

and

56 = 27+29

56 is also part of a Pythagorean triple. Pythagorean triples room sets of 3 number which satisfy:

a2 + b2 = c2

In this case…

332 + 562 = 652

This to represent a right-angle triangle with lengths 33, 56 and also 65, whereby the longest side, or the hypotenuse is 65.

### Did friend Know?

56 is the atomic number of the aspect Barium.

Pythagoreans linked a polygon that 56 sides through Typhon, a Greek mythical creature explained as a monstrous serpentine giant.

It is impossible to construct a perfect constant 56-sided polygon without a computer’s aid; however, a close approximation was discovered at Stonehenge referred to as Aubrey Holes.

In the year 56AD, the war in between Rome and Parthia started due to the invasion of Armenia.

And strangely…There is a city in Arkansas called Fifty-Six!

## To sum Up (Pun Intended!)

Factors divide precisely into a number there is no leaving a remainder. You deserve to express the components of 56 in regards to its element pairs or its prime factors.

The variable pairs the 56 are provided in the form:

(X, Y)

This is because X and Y are two numbers the multiply with each other to do 56.

To discover all the variable pairs, you require to inspect each pair of numbers from 1 to 56, which multiply with each other to do 56. Visit this connect for our printable Divisibility Rules.