Factors

# Factors of 156 | Prime Factorization of 156 | Factor Tree of 156

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 156 | Prime Factorization of 156 | Factor Tree of 156

## Factors of 156

Factors of 156 | Factor Pairs of 156 | Prime factors of 156 |

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78 and 156 | (1, 156), (2, 78), (3, 52), (4, 39), (6, 26) and (12, 13). | 2 × 2 × 3 × 13 |

Calculate Factors of

**The Factors are**

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## What are the factors of 156

Have you ever wanted to know which numbers can be multiplied together to get a specific number? Well, one way we can figure out what those two numbers are is by finding the factors of that given number! Let’s take 156 as an example.

First off, we need to come up with all the potential possibilities for multiplying two whole numbers together and getting 156 – these would be our ‘factors’. To do this efficiently, let’s first use something called square root: it means dividing any squared (for ex., 4 x4) number until you get down its “roots”. It just so happens that when we find the square root of 156, it turns out around 12.3 — so if we create a list from 1-12 then 3 times 51 will equal exactly 156!. This means both 3 and 51 are Factors of156. We also already know that anything divided by itself always equals 1; in other words… since every prime Factorization only has 2 totals – itself plus 1–this tells us right away that anytime dealing with prime Numbers such as 156 his factorization must include ONLY himself +1. And there you have All possible answers for what divides into 156 are:1and151.

## How to Find Factors of 156

The various ways to find the factors of 156 are as follows:

- Factor of 156 using Multiplication Method
- Factors of 156 using Division Method
- Prime Factorization of 156
- Factor tree of 156

## Factors of 156 using Multiplication Method

The Multiplication Method is a great way to find factors of any number. To use it,

- start with the two numbers 1 and 156 and then multiply them together. We can write down this result as our first factor pair (1 x 156 = 156).
- Then we look for other pairs that have the same product when multiplied: like 2 & 78 or 4 & 39 – these are also factor pairs because their multiplication gives us back 162!

So using the Multiplication method, all of the possible factoring combinations for 156 would be (1,156),(2,78 ), (4,39), and (13,12 ).

## Factors of 156 Using Division Method

Let’s talk about finding factors of a number! You know what ‘factors’ mean, right? Factors are numbers that can be multiplied together to get the original number. To find out which numbers make up 156 – let’s use the Division Method!

- We start with our starting point: 156. Then we divide it by 1-156 one by one and see if there is nothing left over after dividing (no remainder) then that means these two numbers fit perfectly like pieces in a puzzle and so they become factors of 156!
- So for example when you divide 78 into 156, there isn’t anything leftover therefore making 78 an answer or factor. Now how cool does this sound!?

The other answers/factors were 1,2 4 & 13 as well so now you know all five possible ways how to split up your beloved whole number 56!!

## Prime Factorization of 156

Calculate Prime Factors of

The Prime Factors of 156 =

2 x

2 x

3 x

13

The process of prime factorization breaks down a large number like 156 into its most basic parts: prime numbers. Prime numbers are special because they can only be divided by themselves and 1. To find the prime factorization for 156,

- We first need to divide it by 2 since that’s the smallest possible prime number; if this division is even (meaning there isn’t any remainder), then 2 is one of our factors! In this case, when you divide 156 by 2 you get 78; so now you know two things—156 = 2×78 and 28 = 2 x 39.
- We keep going with dividing until all those chunks add up to your original number–in this case, 24 multiplied together gives us our final answer.

The prime factors of 156 are 2x2x39=156!

## Factor tree of 156

A factor tree is a really cool tool that can be used to help us find the prime factors of any number! Let’s use it to figure out the prime factors for 156.

- We start by writing 156 at the top of our tree, and then we draw two branches coming from there with numbers 2 and 77 on either side. That’s because those are the smallest whole numbers that divide into 156 without any leftovers (called no remainder).
- Next, since 77 isn’t a prime number like 2 was, we break down each branch further until both sides have only prime numbers listed: 7 and 11 in this case. The process looks something like this: 156 = 2 x 7 x 11.

So these three were all unique combinations of smaller digits that multiplied together and gave us our original number.

## Factor Pairs of 156

Calculate Pair Factors of

1 x 156=156

2 x 78=156

3 x 52=156

4 x 39=156

6 x 26=156

12 x 13=156

13 x 12=156

26 x 6=156

39 x 4=156

52 x 3=156

78 x 2=156

So Pair Factors of 156 are

(1,156)

(2,78)

(3,52)

(4,39)

(6,26)

(12,13)

(13,12)

(26,6)

(39,4)

(52,3)

(78,2)

Did you know that if two numbers are multiplied together, the result can be further broken down into lots of different parts? This is called a factor pair!

For example, if we multiply 1 and 156 together (1 x 156) the answer will be 156. Therefore, our factors for this equation would be 1 and both 56 since these were used to get an outcome of 156. To find out all possible combinations with any number like 154 above –

- Start by dividing it by each whole number from one up until your target value’s square root; in this case, it’s 12 because 12 times 12 = 144 which is less than 154 so anything higher won’t work as a potential solution.
- If there aren’t any remainder after division then write down those answers as their own individual pairs e.g 439 or 78/2 etc. It might seem confusing at first but just remember: when multiplying things back together – what goes in must come out exactly the same meaning you CAN break bigger results into smaller pieces again using addition factoring methods such as those described here today!

## Factors of 156 – Quick Recap

**Factors of 156:** 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156.

**Negative Factors of 156:** -1, -2, -3, -4, -6, -12, -13, -26, -39, -52, -78, and -156.

**Prime Factors of 156:** 2 × 2 × 3 × 13

**Prime Factorization of 156:** 2 × 2 × 3 × 13

## Fun Facts of Factors of 156

- The way we do that is by finding the prime factorization of 156 which are special numbers, called factors, multiplied together to equal it.
- For example 2 x 2 x 39 =156- so in this case there are three factors:2,2 and 39 (each number used only once).
- Any time you have more than two factors when they’re combined together -it makes something bigger –like putting pieces of lego blocks or puzzles together!
- If we list all 8 separate pieces out with 1 being the smallest piece and 156 as our largest “proper” piece then add them up to a total of 348; this is known as an “aliquot sum.” That means no matter how many times you break down a composite number-the total will always be greater than its original value because having each individual smaller part/piece adds up higher.

## Examples of Factor of 156

**1) If a store sold an item for $156, what would the item cost with 8% tax added? Answer:** With 8% tax added the item would cost 168.48 dollars ($156 + ($156 x0.08)= 168.48).

**2) What three consecutive odd numbers have a sum of 156?****Answer: **The three consecutive odd numbers that have the sum of 156 are 51, 53, and 55 (51 + 53 + 55 = 159).

**3) Find two prime numbers which are factors of 156.**Answer: Two prime numbers – 3 and 52 – are factors of 156.

**4) If a store sold 6 items each costing$26 plus 8%tax, how much did they make in total?****Answer: **The store made $ 161.28 in total ((6×26)+((6×26)* 0.08)= 161.28).

**5) How many even numbers are factors of 156? **Answer: Three even numbers – 2, 4, and 78 – are factors of 156.

**6) What is the greatest common factor between 70 and 156? **Answer: The greatest common factor between 70 and 156 is 14.

**7) Divide 156 by its smallest factor to find its largest factor. ****Answer: **Divide 156 by its smallest factor which is 2to find its largest factor; the answer is 78.

**8) Find four consecutive multiples of 7 that add up to 156.****Answer:** The four consecutive multiples of 7 that add up to 156 are 28, 35, 42, and 49 (28 + 35 + 42 + 49 = 154).

**9) In what ways could one divide 155 equal parts so that each part has the same value?****Answer: **One can divide 155 into five equal parts of 31 pieces each or into seven equal parts of 22 pieces each or into fifteen equal parts of 10 pieces each or into thirty-one equal parts of 5 pieces each or into seventy-six equal parts of 2 pieces each into one hundred and fifty-five equal parts of 1 piece each.

**10) What two numbers multiplied together equal 156?Answer:** The two numbers which multiplied together equal 156 are 4 and 39 (4 × 39 =156).

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## Frequently Asked Questions on Factors of 156

**What is the factor of 156?**

The factors of 156 are 1, 2, 4, 39, 78, 156.

**How many factors does 156 have?**

156 has six factors – 1, 2, 4, 39, 78, and 156.

**What is the greatest common factor between 70 and 156?**

The greatest common factor between 70 and 156 is 14.

**How can I divide 155 into equal parts so each part has the same value?**

You can divide 155 into five equal parts of 31 pieces each or into seven equal parts of 22 pieces each or into fifteen equal parts of 10 pieces each or into thirty-one equal parts of 5 pieces each or into seventy-six equal parts of 2 pieces each or into one hundred and fifty-five equal parts of 1piece each.

**Are there any even numbers that are factors of 155?**

Yes, two even numbers – 2 and 78 – are factors of 155.

** In what ways could one double a number and then divide it by its greatest factor to get the same number back?**

If you double a number and then divide it by its greatest factor (i.e., its largest prime factor), you will get the same number back. For example, if you double 155 to 310 and then divide it by its greatest factor (31), the result will still be

10.

**What two prime numbers multiplied together equal 154?**

The two prime numbers multiplied together equal 154 are 17 and 11(17×11=187).

**What three consecutive odd integers have a sum of 156?**

The three consecutive odd integers whose sum equals 156 are 51, 53, and 55(51+53+55=159).

**Find two consecutive multiples of 31 that multiply together to produce 155.**

The two consecutive multiples of 31 that multiply together to produce 155 are 31 and 62(31×62=1922).

**If Mary was given $155 at a store for free, how much money could she buy for her three friends with an 8% tax added?**

With an 8% tax added Mary could buy items worth $ 167.40 ($155 + ($155 x 0.08)= 167.40). As such, she could buy items worth $ 55.80 each (3 x55.80 = 167.40) for her three friends with the given amount.

Written by by

Prerit Jain