According come Aristotle, 56 is the variety of layers of the Universe. He organized that earth is the first layer, v 55 crystalline spheres above it.

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

If you desire a quick reference for factors, this factors and multiples table will certainly be an ext useful.

A factor is a number the goes into another number perfectly. For example, 2 is a element of 10 since it goes into 10 perfectly there is no leaving a remainder.

If you main point 2 by 5, you acquire 10, which method both 2 and 5 are determinants of 10.

You will discover out what 56’s determinants are, exactly how to find factor pairs and all about prime factorization in this lesson.

Once you recognize this, friend will be able to find the factors of any number!

Contents

56’s components Pairs Primes Factorizing 56 how to find 56’s factors Prime Factorization isn’t 56 Interesting? To amount Up (Pun Intended!)

## All the components of 56

The factors of 56 room **1, 2, 4, 7, 8, 14, 28, and also 56**.

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

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

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

### Factor pairs of 56

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

Factor pairs space sets of two numbers the multiply with each other to make an additional number.

So you require to find out which two numbers, ** X** and also

**multiply together to make 56. This is composed as:**

*Y*(

*X*,

*Y*)

variable Pairs of 56

(1, 56) (2, 28) (4, 14) (7, 8)

Sometimes you deserve to include an unfavorable numbers together a factor since when two an adverse numbers room multiplied together, they make a confident number!

It is important to remember that both numbers should be negative to do a hopeful number. If among them is negative, and one of lock is positive, they will certainly be negative.

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

You have probably noticed that the negative factors space the same as the confident ones, just they’re negative!

However, just the confident ones are being referred to unless said otherwise once talking about the variable pairs.

### Is 56 Abundant?

If the sum of the positive determinants is bigger than twice the number itself, it is known as one **abundant number**.

The sum of the positive factors is:

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

Double 56 is 112, and the sum of every its factors is 120. This renders 56 an numerous number: the amount of its factors is better than double itself.

### Prime determinants of 56

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

3 ÷ 1 = 3 3 ÷ 3 = 1

3 can not be separated by anything else so that is a prime number.

56 has only two prime factors, which space 2 and also 7.

You deserve to use this prime factors to write 56 together a product that its element factors.

56=2 × 2 × 2 × 7

You can work this the end by using any type of two variable pairs and also keep dividing them down till you have actually prime numbers.

This is a **factor tree**. The starts v the original number at the top, which is broken down into aspect pairs.

When a element is found, it is circled and also the other number is broken down further.

The prime number, 2, appears 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 deserve to express 56 together the sum of consecutive primes.

56 = 3 + 5 + 7 + 11 + 13 + 17

Why discover the prime Factors?

Finding all the prime factors of a number deserve to be helpful in finding the **Greatest typical Factor** (**GCF**) of two numbers, as well as the **Least common Multiple** (**LCM**) of 2 numbers.

Prime factorization is also useful in the real civilization in cryptography. It can take an exceptionally long time to discover a big number’s element factorization, even for computers!

## Factorizing 56

### How to discover the components of 56

To find all the factors, you must start through 1 and work v each number one through one come 56, check if over there is a remainder once 56 is split by each number. If over there is no remainder, the number is a factor.

Each time you find a factor pair, you mitigate the expression of determinants you are trying to find to numbers within such aspect pair intervals.

We will certainly share a few tricks through you to do this a rapid job.

The Processbeginning at 1…

56 ÷ 1 = 56

There is no remainder, so girlfriend have evidenced 1 and 56 room a aspect pair. Friend now need to uncover factors between 1 and also 56.

56 ÷ 2 = 28

So, 2 and 28 are a variable pair. You now require to uncover factors in between 2 and also 28.

56 ÷ 3 = 18.67

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

You will view there space no determinants up to 6.

56 ÷ 7 = 56

7 and 8 are a aspect pair. There space no integers between 7 and also 8, so girlfriend have discovered all the factor pairs that 56.

So, in complete you have the adhering to factors:

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

Here space a couple of tricks for spotting factors:

All integers have a factor of 1Any also number has actually a variable of 2If the sum of the number of a number is a lot of of 3 climate 3 is a factorNumbers v a factor of 4 should be even and if the last two digits room 00 or divisible by 4 then 4 is a factorAny number with the last digit 0 or 5 has actually a factor of 5Any number that is even and also the sum of that is digits space a multiple of 3 will have actually a element of 6There no a basic trick for spotting determinants of 7!If the last 3 number of a number are divisible by 8 the will have a factor of 8If the amount of a number’s number is a multiple of 9 then it has actually a variable of 9Numbers with the last digit 0 will have actually a element of 10These are so valuable in fact, that us made a printable table that the divisibility rule from 2 to 15, add to a worksheet to practice, for you to store with you–for your own use. Simply click or tap the pictures below!

Now, part practice.

making use of the an approach above, uncover the factors of: a) 24 b) 37 c) 72 (Open to display solutions)a) 1, 2, 3, 4, 6, 8, 12, 24

b) 37 is a prime number, for this reason 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 every the prime numbers which multiply together to do the original number.

The easiest an approach to find all the element numbers is to usage a prime factor tree.

At the start of the tree, you have 56.

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

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

As 2 is a prime number, you can circle it to show it is the final variable on this branch, and it can not be split anymore.

Now you require to proceed breaking down 28 into its determinants by finding the smallest prime number that divides 28.

It is divisible by 2 again, so…

Again 2 have the right to be circled. You still need to malfunction 14, which, together it turns out, is divisible by 2 again!

Both 2 and also 7 space prime numbers, for this reason you have the right to circle both.

Just prefer the variable tree girlfriend were shown before, the end of every branch is circled, so you have actually completed your very own prime aspect tree!

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

56 = 2 × 2 × 2 × 7

This can be neatened up by using the power or exponent form:

56 = 23 × 7

write each number as a product of its element factors. A) 48 b) 90 c) 104 (Open to display 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 ways of expressing 56, other than the factors, together it has some amazing properties.

56 is the sum of the an initial 6 triangle numbers.

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

A triangle number counts objects arranged in an equilateral triangle.

This provides 56 the sixth tetrahedral number together it is the sum of the first 6 triangular numbers, making it a triangle pyramidal number.

You can likewise express 56 together the sum of consecutive even or weird numbers.

For also numbers…

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

For weird numbers…

56 = 11+13+15+17

and

56 = 27+29

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

a2 + b2 = c2

In this case…

332 + 562 = 652

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

### Did you Know?

56 is the atomic variety of the element Barium.

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

It is impossible to construct a perfect continuous 56-sided polygon there is no a computer’s aid; however, a near approximation was found at Stonehenge dubbed 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 amount Up (Pun Intended!)

Factors divide exactly into a number there is no leaving a remainder. You can express the factors of 56 in terms of its aspect pairs or its prime factors.

The variable pairs the 56 are provided in the form:

(

*X*,

*Y*)

This is since ** X** and also

**are two numbers the multiply with each other to make 56.**

*Y*To uncover all the aspect pairs, you need to inspect each pair of number from 1 to 56, which multiply together to make 56. Visit this link for our printable Divisibility Rules.

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You discovered that the factors of 56 space **1, 2, 4, 7, 8, 14, 28 and 56**.

Please leave a comment below if girlfriend have any questions and let us know just how you did through the challenges!