Factors

# Factors of 162 | Prime Factorization of 162 | Factor Tree of 162

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 162 | Prime Factorization of 162 | Factor Tree of 162

## Factors of 162

Factors of 162 | Factor Pairs of 162 | Prime factors of 162 |

1, 2, 3, 6, 9, 18, 27, 54, 81 and 162 | (1,162), (2,81), (3,54), (6,27), and (9,18) | 2 × 3 × 3 × 3 |

Calculate Factors of

**The Factors are**

## What are the factors of 162

Do you know what special numbers can help us find out all the factors of a larger number? These special numbers are called “factors”. For example, do you remember when we had to break up 162 into little pieces and multiply them together so that it became equal to 162 again? All those pieces were the Factors of 162. Let’s look at an example! The Factors 1, 2, 3 , 6, 9,18, 27 54 81 &162 are divided evenly into our original number – they fit perfectly like puzzle pieces without leaving any extra over. That way if use two or more of these factors then using multiplication will result in getting back our starting point (in this case) which is also known as ‘the product.’

## How to Find Factors of 162

The major methods through which we can find the factors of 162 are as follows:

- Factor of 162 using Multiplication Method
- Factors of 162 using Division Method
- Prime Factorization of 162
- Factor tree of 162

## Factors of 162 using Multiplication Method

Let’s pretend the number 162 is like a box that we want to open. The only way to do this is by finding two numbers that when multiplied together, equal 162—just like if you wanted to unlock a safe, you would need two keys that work together! To find these special ‘keys’, called factors of the number 162 in Math talk, we can use something called the multiplication method – basically, it means covering all our bases and trying different things until they fit perfectly! After testing out various combinations (in other words, multiplying them!), we found 5 pairs of “keys” or factors:

(1 x162), (2×81), (3×54), (6×27), and finally 9 x 18–once combined produce exactly what was inside the box…aka an answer of one hundred sixty-two!.

## Factors of 162 Using Division Method

Have you ever wondered how to find all the factors of a number? Finding these can be tricky but there is a simple method. It’s called the division method!

Think about it this way – let’s say we have an apple that needs to be shared amongst three people, so each person gets one-third or one-third of an apple. The same process happens with numbers too! We divide them by certain other values and check if they give us whole pieces (no remainder). If yes, then those divisors are considered as factors because when multiplied together get us our original value, just like when sharing apples between 3 people: 1/3 + 1/3 +1 / 3 = Our Original Apple. So going back to the factorization approach; we try dividing our number sequentially starting from 1 until its square root which will tell us if any part of it was cleanly divided without leaving remainders in portions such as 2 thirds instead of being able to equalize into something simpler like 6 sixths for example where both sides split evenly(Remainder Zero).

## Prime Factorization of 162

Calculate Prime Factors of

The Prime Factors of 162 =

2 x

3 x

3 x

3 x

3

Prime factorization is a way to break down numbers into the building blocks they are made up of. To find out what makes 162, we start by dividing it by smaller prime numbers (2, 3, 5, and 7). If we can’t divide evenly without having some leftovers then that number isn’t part of the answer – so when divided 2 doesn’t work; nor does 3 or 9. But finally when you get to 27 ÷3 =9 and lastly 9÷3=3 – which IS a prime number! That’s our first piece for making 162: two times three raised to four power (2×34), meaning that ultimately if all those pieces were put together in order – 2 x 3 x 3 x 3×3- you’d end up with your original whole:162.

## Factor tree of 162

It can be confusing when trying to figure out how many of which prime number makes up a big one. A factor tree is a perfect tool for this! It’s like a diagram with branches that help you track down what numbers make up any given number, all the way down until it’s just primes left – and even then if they’re squared or cubed too. Let’s look at an example: 162 has 2 x 81 =162 as its first branch – so we know our final answer will have two twos in there somewhere – but why? If your question is ‘What are all the prime factors inside this bigger number?’ You’ll need to keep breaking it apart along those branches until you reach small enough pieces only made from single-digit primes (3, 5 7, etc). In this case, after starting with two times eighty-one…we get 3×27=81; 3×9=27; and finally three threes equals nine…2*2*3*3 = 36 Voila — Two twos and two threes now add together equal twenty-four!

## Factor Pairs of 162

Calculate Pair Factors of

1 x 162=162

2 x 81=162

3 x 54=162

6 x 27=162

9 x 18=162

18 x 9=162

27 x 6=162

54 x 3=162

81 x 2=162

So Pair Factors of 162 are

(1,162)

(2,81)

(3,54)

(6,27)

(9,18)

(18,9)

(27,6)

(54,3)

(81,2)

When you have a number, such as 162, there are numbers that can be multiplied together to get the original number. For example: if you multiply 1 and 162 together it equals 162; 2 times 81 is also equal 162; 3 times 54 is also equal to 152 (and so on). These pairs of whole numbers which when combined give us our original number called “factor pairs”. In this case, our factor sets for 162 include (1,162 ),(2,81), (3,54 ), etc… When we find factors like these they come in two parts – one part being reflected exactly opposite from the other side – making them mirror images reflecting each other! So remember that every single pair has an inverse or reflection – just like how your face looks the same while looking into a mirrored glass with a reversed view.

## Factors of 162 – Quick Recap

**Factors of 162:** 1, 2, 3, 6, 9, 18, 27, 54, 81 and 162.

**Negative Factors of 162:** 1, -2, -3, -6, -9, -18, -27, -54, -81, and -162.

**Prime Factors of 162:** 2 × 3 × 3 × 3

**Prime Factorization of 162:** 2 × 3 × 3 × 3

## Fun Facts of Factors of 162

- It’s part of many different Mathematical patterns. For example, the factors of 162 are 1, 2, 3, 6, 9, 18, and so on until we get to 81 and finally arrive at 16!
- You can also find it in triangular numbers which have three sides like a triangle shape – when you add together the squares of these first three triangles (1 + 3^2 + 6^2), they all equal up to be exactly 162.
- Another thing about this amazing number is that it’s called a ‘Harshad Number’ because if you split up each digit and then add them back together again their sum must divide into 162 without any remainder i(e 1+6+2=9).
- And last but certainly not least – did I tell you already how cool Fibonacci Numbers are? Well, when you put two Fibonacci cubes side-by-side with one another: (1 ^3 plus 2 ^3) what do you think would happen!? That’s right; both those cubes added together = glorious beautiful magical wonderful lovely spectacular KABOOM!!! Aka ……162!

## Examples of Factor of 162

**1) Rahul has 162 marbles. He wants to divide them among his 6 friends. How many marbles will each friend get?****Answer: **Each friend will get 27 marbles.

**2) Abi has 162 chocolate bars. She wants to give away an equal number of bars to each of her 8 siblings. How many chocolate bars will each of her siblings get?****Answer: **Each sibling will get 20 chocolate bars.

**3) Cara needs 162 pieces of paper for her art project. If she packs them into 12 boxes, how many pieces of paper will be in each box?****Answer:** Each box will have 13 pieces of paper.

**4) Jake has a bag of 162 coins that he wants to share with his class. If there are 24 students in the class, how many coins will each student receive?****Answer:** Each student will receive 7 coins.

**5) Beth has a container with 162 nuts. She wants to distribute them evenly among 10 jars her family members can use as snacks. How many nuts should go in each jar?****Answer: **There will be 16 nuts in each jar.

**6) Ryan has a collection of 162 stamps that he wants to display on 6 different boards in his room. How many stamps should he put on each board?****Answer: **Ryan should put 27 stamps on each board.

**7) Lucy found 162 seashells on the beach and she wants to put them into 9 containers for a project at school. How many shells should go into each container?****Answer: **Each container should have 18 shells in it.

**8) Tom has 161 books and he wants to sort them into 8 piles so that he can organize them better on his shelves at home. How many books should be in each pile?****Answer:** Each pile should have 20 books in it.

**9) Abigail has collected 162 pebbles from the garden and wants to divide them equally between 13 jars for decoration purposes. How many pebbles should go in each jar?Answer: **Each jar will get 12 pebbles in it.

**10 Jayden had bought 162 pencils and he wanted to distribute them among 17 people working with him. How many pencils should he give out per person?**

Answer:He would give out 9 pencils per person.

Answer:

## Frequently Asked Questions on Factors of 162

**What is a factor of 162? **

A factor of 162 is a number that divides evenly into 162. The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, and 162.

**What are the prime factors of 162?**

The prime factors of 162 are 2 and 81.

**How many even factors does 162 have?**

There are five even factors of 162: 2, 6, 18, 54, and 162.

**How many odd factors does 162 have?**

There are four odd factors of 162: 1, 3, 9, and 27.

**Can 161 be divided by 8? **

No, 161 cannot be divided by 8 as it leaves a remainder when divided.

**Are 4 and 81 both factors of 162?**

Yes, 4 and 81 are both factors of 162.

**Is 10 a factor of 162?**

No 10 is not a factor of 162.

**Is 63 a factor of 162?**

No 63 is not a factor of 162.

**Is 7 a multiple of 81?**

Yes 7 is a multiple of 81 because 7×81 = 567 which is divisible by 81 with no remainder.

**Is 66 a multiple of 54?**

No 66 is not a multiple of 54 because 66×54=3564 which has a remainder when divided by 54.

Written by

Prerit Jain