Factors

# Factors of 152 | Prime Factorization of 152 | Factor Tree of 152

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 152 | Prime Factorization of 152 | Factor Tree of 152

## Factors of 152

Factors of 152 | Factor Pairs of 152 | Prime factors of 152 |

1, 2, 4, 8, 19, 38, 76, 152 | (1, 152), (2, 76), (4, 38), (8, 19) | 2^3×19 |

Calculate Factors of

**The Factors are**

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## What are the factors of 152

To find the factors of 152, we can use either division or multiplication. With division, start by dividing 152 by prime numbers starting with 2 and continuing until you get a reminder that’s not 0 – this will tell us which numbers are (and aren’t) factors of our number. We divide 152 once to get 76; then again for 38; yet another time for 19; but when we divided 6 from 19 there was 1 left over so 3 is NOT a factor! The same thing happened when trying 5 and 7 too – they don’t work as factors either! So altogether, the four true factors of 152 are 2 x 2 x2x19 =152

## How to Find Factors of 152

The main methods through which we can find the factors of a number are given below and those methods can be used to find the factors of 152. Those methods are as follows:

- Factor of 152 using Multiplication Method
- Factors of 152 using Division Method
- Prime Factorization of 152
- Factor tree of 152

## Factors of 152 using Multiplication Method

If you want to find the factors of a number, like 152 in this example, then try out the multiplication method!

- Start by writing down all of the numbers between 1 and up until just before your number (in our case it’s 12.2).
- Then go through that list one at a time and see if any can be divided evenly into 152 – meaning there is no remainder when they are divided.
- If so, those numbers are called “factors” because each factor multiplied together makes your original starting number – so 2 x 2 x 2 x 19 =152. Give it a shot with different numbers too!

## Factors of 152 Using Division Method

Let’s say you want to know what the factors of 152 are. To find out, we can use something called the division method! It helps us divide numbers by smaller prime numbers starting with 2 – like a puzzle where each answer provides clues for further questions until it finally leads us to an answer.

In this case,

- First, we divided 152 by 2 which yields 76 and no remainder so that means one factor is two itself (2). Then when dividing again into 76 since there was still no remainder left then another factor turns up being two as well (2)!
- We repeated this process several times until our quotient result turned out 1 meaning we had gone through all possible combinations leaving only the true factors behind: namely twice-two plus 19 making them in total four altogether – or put differently these would be your final answers -> {2 x 2 = 4; 19 x 1 = 19}.

## Prime Factorization of 152

Calculate Prime Factors of

The Prime Factors of 152 =

2 x

2 x

2 x

19

To figure out the prime factorization of a number, like 152, you can use either division or multiplication. To explain this to 5th graders: think about it as a grouping in terms of their smallest parts. Let’s do an example using division with 152 starting from its smallest part which is 2! We keep dividing by two until there are no more remainder left (or when our remainder becomes 1). This means that we divided all the way down and every time we divide something by 2 it has to be even so once our numbers reach odd then those ones don’t get factored into the original number. For 152 these were divided evenly -2)(76)(38)(19)- meaning that each one was divisible exactly twice making them factors for checking how many times your answer will fit back into 146! That’s why the Prime Factorization for 7245 is written as; “152 = (2 x 2 x 38)”, showing us how broken down 176 is when split up into its simplest form possible-greater than what cannot be separated any further.

## Factor tree of 152

When you are trying to figure out the factors of a number, like 152 for example, it can be helpful to draw something called a Factor Tree.

- To make one start by writing down your number—in this case it’s 152–then put a box around it.
- Since not all numbers have prime factors we need to check if our number is also prime; in this case152 isn’t so divide that first factor (2) from the original and write 76 in another box under or next to what you wrote before with 2 beside it because that was the factor used!
- Then take those two boxes and do steps 3-5 again until no more dividers can come into play which means there aren’t any other possible numbers since they would all be the factors of the original, right?

So when making our tree here: go ahead & keep dividing but watch out once someone comes up as “prime.”

## Factor Pairs of 152

Calculate Pair Factors of

1 x 152=152

2 x 76=152

4 x 38=152

8 x 19=152

19 x 8=152

38 x 4=152

76 x 2=152

So Pair Factors of 152 are

(1,152)

(2,76)

(4,38)

(8,19)

(19,8)

(38,4)

(76,2)

Understanding factor pairs can be fun and help you better understand the multiplication process. Let’s use 152 as an example to get started.

- To find all its possible factor pairs we will have to break it down into smaller factors, like 2 and 76 or 19 times 8! All of these combinations give us a total that is equal to our original number – in this case, 152!
- We call each one of those combinations a “factor pair”. You may also notice that some of these combinations are able to repeat themselves (like with 2 &2). That’s because when using the same factors just switching their order still gives us our starting total – so they count twice since both those options add together for 152!

## Factors of 152 – Quick Recap

**Factors of 152:** 1, 2, 4, 8, 19, 38, 76, 152

**Negative Factors of 152:** -1, -2, -4, -8, -19, -38, -76, -152.

**Prime Factors of 152:** 2^3×19

**Prime Factorization of 152:** 2^3×19

## Fun Facts of Factors of 152

- 152 is just such an example! It’s special because it can break down into four different factors: 2^3 * 19.
- Being even also means the last digit of this unique number will always end in an “even” digit like 0,2 or 4…pretty cool right?!
- This makes it useful for solving various kinds of mathematical problems and computations as well as understanding how numbers interact with each other.

## Examples of Factor of 152

**1) What is the greatest common factor between 70 and 152?****Answer: **The greatest common factor between 70 and 152 is 4.

**2) Find four consecutive multiples of seven that add up to 152.****Answer: **The four consecutive multiples of seven that add up to 152 are 7, 14, 21, and 28 (7 + 14 + 21 + 28 = 80).

**3) What two numbers multiplied together equal 152?****Answer: **The two numbers multiplied together which will be equal to 152are8 and 19 (8 × 19 = 152).

**4) Divide 152 by its largest factor to find its smallest factor. ****Answer:** Divide 152 by its largest factor which is152to find its smallest factor; the answer is 1.

**5) If a store sold a product for $152 before tax, how much would it cost with 8% tax added? ****Answer:** With 8% tax added the product would cost 164.16 dollars ($152 + ($152 x 0.08)= 164.16).

**6) Rachel purchased 5 items at a store for $30 each plus tax at 8%. How much did she spend with tax included?****Answer: **With tax included Rachel spent 163.20 dollars ((5×30)+((5×30)* 0.08)= 163.20).

**7) Find three consecutive even integers whose sum equals 153.****Answer: **The three consecutive even integers whose sum equals 153 are 76, 78, and 80 (76 + 78 + 80= 234).

**8) Find two consecutive odd numbers whose product is equal to 153.****Answer: **The two consecutive odd numbers whose product is equal to 153 are 17 and 19 (17 × 19 = 323).

**9) How many prime numbers are factors of 152? Answer:** Four prime numbers – 2, 3, 7, and 11 – are factors of 152.

**10) What are the factors of 152?**

**Answer:** The factors of 152 are 1, 2, 4, 8, 19, 38, 76, and 152

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## Frequently Asked Questions on Factors of 152

**What is the greatest common factor between 70 and 152?**

The greatest common factor between 70 and 152 is 4.

**What two numbers multiplied together equal 152?**

The two numbers multiplied together equal 152 are 8 and 19 (8 × 19 = 152).

**Find four consecutive multiples of seven that add up to 152.**

The four consecutive multiples of seven that add up to 152 are 7, 14, 21, and 28 (7 + 14 + 21 + 28 = 80).

** Divide 152 by its largest factor to find its smallest factor.**

Divide 152 by its largest factor which is152to find its smallest factor; the answer is 1.

**If a store sold a product for $152 before tax, how much would it cost with 8% tax added?**

With 8% tax added the product would cost 164.16 dollars ($152 + ($152 x0.08)= 164.16).

**What are the factors of 152?**

The factors of 152 are 1, 2, 4, 8, 19, 38, 76, and 152.

**How many prime numbers are factors of 152?**

Four prime numbers – 2, 3, 7, and 11 – are factors of 152.

**Find three consecutive even integers whose sum equals 153.**

The three consecutive even integers whose sum equals 153 are 76, 78, and 80 (76 + 78 + 80= 234).

**Find two consecutive odd numbers whose product is equal to 153.**

The two consecutive odd numbers whose product is equal to 153 are 17 and 19 (17 × 19 = 323).

**Rachel purchased 5 items at a store for $30 each plus tax at 8%. How much did she spend with tax included?**

With tax included Rachel spent 163.20 dollars ((5×30)+((5×30)* 0.08)= 163.20).

Written by

Prerit Jain