According come Aristotle, 56 is the number of layers that the Universe. He hosted that planet is the very first layer, through 55 crystalline spheres over it.

You are watching: 56 as a product of prime factors

This lesson will certainly walk you with all 56’s factors, how to uncover the factors and other interesting factor facts!

If you want a fast reference because that factors, this factors and also multiples table will certainly be much more useful.

A element is a number that goes into an additional number perfectly. For example, 2 is a factor of 10 since it goes right into 10 perfectly there is no leaving a remainder.

If you main point 2 through 5, you obtain 10, which means both 2 and 5 are factors of 10.

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

Once you understand this, you will be able to find the components of any kind of number!

Contents

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

## All the factors of 56

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

56 have the right to be split by itself and also one, however it is also divisible by other numbers, so the is a **composite number**, and there are more than two factors!

As you have actually just learned, a **factor** is one number that divides another without leave a remainder.

You have the right to write a number in regards to its factor pairs or a product the its element factors.

### Factor pairs of 56

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

Factor pairs room sets of two numbers that multiply with each other to make another number.

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

**multiply together to do 56. This is written as:**

*Y*(

*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 due to the fact that when two an adverse numbers room multiplied together, they do a hopeful number!

It is important to remember that both numbers need to be an adverse to make a optimistic number. If among them is negative, and also one of castle is positive, they will certainly be negative.

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

You have probably noticed the the negative factors are the same as the positive ones, just they’re negative!

However, just the optimistic ones are being described unless stated otherwise when talking about the variable pairs.

### Is 56 Abundant?

If the amount of the positive components is bigger than twice the number itself, that is well-known as one **abundant number**.

The sum of the positive components is:

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

Double 56 is 112, and the amount of every its determinants is 120. This makes 56 an abundant number: the amount of its components is higher than dual itself.

### Prime determinants of 56

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

3 ÷ 1 = 3 3 ÷ 3 = 1

3 cannot be divided by anything rather so it is a prime number.

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

You can use this prime factors to create 56 together a product the its element factors.

56=2 × 2 × 2 × 7

You deserve to work this the end by using any two variable pairs and keep dividing them down till you have actually prime numbers.

This is a **factor tree**. It starts v the initial number at the top, i beg your pardon is broken down into aspect pairs.

When a prime is found, that is circled and the various other number is damaged down further.

The element number, 2, appears on 3 occasions, so this have the right to be written much more simply using power or exponent form.

56 = 23 × 7

The number 56 additionally has various other prime numbers. You can express 56 as the sum of consecutive primes.

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

Why uncover the prime Factors?

Finding all the prime determinants of a number have the right to be beneficial in finding the **Greatest usual Factor** (**GCF**) of 2 numbers, and the **Least typical Multiple** (**LCM**) of 2 numbers.

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

## Factorizing 56

### How to find the components of 56

To uncover all the factors, you have to start v 1 and also work with each number one by one come 56, checking if over there is a remainder as soon as 56 is divided by each number. If there is no remainder, the number is a factor.

Each time you uncover a element pair, you alleviate the interval of determinants you are trying to find to numbers within such aspect pair intervals.

We will share a couple of tricks v you to make this a quick job.

The Processstarting at 1…

56 ÷ 1 = 56

There is no remainder, so you have confirmed 1 and 56 space a variable pair. Girlfriend now need to find factors between 1 and 56.

56 ÷ 2 = 28

So, 2 and 28 are a factor pair. Friend now need to find factors between 2 and 28.

56 ÷ 3 = 18.67

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

You will see there room no factors up to 6.

56 ÷ 7 = 56

7 and 8 space a element pair. There room no integers in between 7 and also 8, so girlfriend have discovered all the element pairs that 56.

So, in complete you have the following factors:

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

Here space a few tricks for spotting factors:

All integers have a element of 1Any even number has actually a aspect of 2If the sum of the number of a number is a many of 3 then 3 is a factorNumbers through a aspect of 4 need to be even and also if the last two digits space 00 or divisible by 4 then 4 is a factorAny number through the critical digit 0 or 5 has a factor of 5Any number that is even and also the sum of the digits are a multiple of 3 will have actually a variable of 6There no a an easy trick for spotting components of 7!If the critical 3 number of a number space divisible by 8 it will have a element of 8If the amount of a number’s number is a multiple of 9 climate it has actually a factor of 9Numbers through the critical digit 0 will have a aspect of 10These space so helpful in fact, that we made a printable table the the divisibility rules from 2 to 15, plus a worksheet come practice, for you to store with you–for your own use. Simply click or insanity the pictures below!

Now, part practice.

using the an approach above, find the factors of: a) 24 b) 37 c) 72 (Open to show solutions)a) 1, 2, 3, 4, 6, 8, 12, 24

b) 37 is a prime number, so the only determinants are 1, 37

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

### Prime Factorization

Prime factorization is finding all the element numbers i m sorry multiply with each other to make the initial number.

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

At the begin of the tree, you have 56.

Begin by picking two element pairs that multiply together to make the number.

Choose the aspect pair through the smallest prime number in it, e.g., 2 and also 28, and add them as branches come the tree.

As 2 is a element number, you deserve to circle the to present it is the final aspect on this branch, and it can not be divided anymore.

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

It is divisible by 2 again, so…

Again 2 have the right to be circled. Friend still require to break down 14, which, as it turns out, is divisible through 2 again!

Both 2 and also 7 are prime numbers, for this reason you can circle both.

Just favor the element tree friend were presented before, the finish of every branch is circled, therefore you have completed your own prime variable tree!

You can now refer 56 as a product of the circled element factors.

56 = 2 × 2 × 2 × 7

This have the right to be neatened increase by making use of the power or exponent form:

56 = 23 × 7

write each number as a product that 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 means of expressing 56, other than that factors, together it has some interesting properties.

56 is the amount of the first 6 triangular numbers.

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

A triangular number counts objects i ordered it in an it is intended triangle.

This makes 56 the sixth tetrahedral number as it is the amount of the first 6 triangular numbers, making it a triangular pyramidal number.

You can additionally express 56 together the amount of consecutive even or strange 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 space sets the 3 numbers which satisfy:

a2 + b2 = c2

In this case…

332 + 562 = 652

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

### Did girlfriend Know?

56 is the atomic variety of the aspect Barium.

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

It is difficult to construct a perfect continuous 56-sided polygon without a computer’s aid; however, a nearby approximation was uncovered at Stonehenge called Aubrey Holes.

In the year 56AD, the war between Rome and Parthia started because of the intrusion of Armenia.

And strangely…There is a city in Arkansas referred to as Fifty-Six!

## To sum Up (Pun Intended!)

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

The factor pairs the 56 are given in the form:

(

*X*,

*Y*)

This is because ** X** and

**room two numbers that multiply with each other to make 56.**

*Y*To uncover all the aspect pairs, you need to examine each pair of numbers from 1 to 56, i beg your pardon multiply together to make 56. Visit this attach for our printable Divisibility Rules.

See more: Vector Mechanics For Engineers Statics 11Th Edition Pdf, Vector Mechanics For Engineers

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

Please leaving a comment listed below if friend have any type of questions and let us know how you did v the challenges!