Factors

# Factors of 153 | Prime Factorization of 153 | Factor Tree of 153

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 153 | Prime Factorization of 153 | Factor Tree of 153

## Factors of 153

Factors of 153 | Factor Pairs of 153 | Prime factors of 153 |

1, 3, 9, 17, 51, 153 | (1, 153), (3, 51), (9, 17) | 3×17 |

Calculate Factors of

**The Factors are**

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## What are the factors of 153

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 153 as an example.

First off, we need to come up with all the potential possibilities for multiplying two whole numbers together and getting 153 – 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 153, it turns out around 12.3 — so if we create a list from 1-12 then 3 times 51 will equal exactly 153! This means both 3 and 51 are Factors of 153. 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 a prime number such as 154 his factorization must include only himself +1. And there you have All possible answers for what divides into 153 are:1and153.

## How to Find Factors of 153

The methods of finding the factors of 153 are as follows:

- Factor of 153 using Multiplication Method
- Factors of 153 using Division Method
- Prime Factorization of 153
- Factor tree of 153

## Factors of 153 using Multiplication Method

If you want to find the factors of 153 using multiplication, it’s really easy!

- First off, make a list with all the numbers from 1 up until around 12.3 (which is close to the square root of 153).
- Then go through and divide each number in your list into 153 – if there isn’t any remainder then that means it’s one of its factors.
- You’ll soon see that both 1 and 153 are divisible by 3 evenly so those two must be our answer; this also proves that 153 is a prime number since no other factor could have been greater than 12.3 when we divided them out earlier!

## Factors of 153 Using Division Method

To find the factors of a number means to figure out which numbers, when multiplied together, can create that same original number. There’s an easy way to do this called the division method!

Let’s take 153 as an example –

- we start by dividing it by 2 (the smallest prime number). We get 76 with 1 remaining so 2 isn’t a factor.
- So then try 3 instead – and we get 51 without any leftovers! That makes sense since 3 times 51 is exactly equal to 153 – so 3 IS one of our factors for 153.

Since 51 is also a prime number though, there won’t be any more whole-number answers if you keep on dividing like before…so what does this mean? - It just tells us that 153 only has two factors: 1 PLUS itself! This happens whenever you’re dealing with prime numbers – they have no other answer but themselves and “1″.

## Prime Factorization of 153

Calculate Prime Factors of

The Prime Factors of 153 =

3 x

3 x

17

Finding the prime factorization of a number is like taking it apart into its simplest building blocks! To find out what those building blocks for 153 are, we can use two different methods – divide or multiply. Let’s try dividing first:

- We start by finding all of the special ‘prime’ numbers that make up 152 – these are only divisible by themselves and 1 (like 2, 3 & 5).
- When divided this way from smallest to biggest we’ll get 76 with a remainder of one; when divided again with 3 you will get 51 with no remainder left over meaning 3 was part of our answer.
- Since 51 is also considered a prime number itself however and has no other factors which give us quotients not equal to 1 then 151 must be composed solely of itself making it entirely “Prime”. So in summation…153=153!

## Factor Tree of 153

Factor tree of 153 is a method of finding the prime factors of a number by dividing it repeatedly by smaller prime numbers. The process starts by dividing 153 by the smallest prime number, 3, which results in 51. Then, 51 is divided by 3 again, resulting in 17. Since 17 is a prime number, the factor tree is complete and the prime factors of 153 are 3 and 17.

## Factor Pairs of 153

Calculate Pair Factors of

1 x 153=153

3 x 51=153

9 x 17=153

17 x 9=153

51 x 3=153

So Pair Factors of 153 are

(1,153)

(3,51)

(9,17)

(17,9)

(51,3)

Finding factor pairs of a number is like playing detective and piecing together clues! For example, if the original number is 153 – what two numbers when you multiply them together give us that answer?

- To find out we can start by writing down all possible factors for 153. That’s easy because every single number has 1 as its first partner in crime so our list looks something like this: (1,153).
- Now one side of each equation always stays the same but guess who doesn’t? Yup – it’s 1!
- So now we just need to pair up which other numbers could possibly be involved with 1.
- In this case, there are no other suspects needed since both sides add up to make an even total; giving us only one set of Factor Pairs – (1,153)!

## Factors of 153 – Quick Recap

**Factors of 153:** 1, 3, 9, 17, 51, 153

**Negative Factors of 153:** -1, -3, -9, -17, -51, and -153.

**Prime Factors of 153:** 3×17

**Prime Factorization of 153:** 3×17

Fun Facts of Factors of 153

- It’s the only one with just two factors: 1 and itself. That means it can’t be divided by anything other than these numbers without leaving some leftover – kind of like when you cut up the cake for 5 people but there are 3 pieces left over at the end – except we don’t get any yummy cake here, sadly!
- 153 also has another cool trick – if we cube each digit (so write down “1 cubed plus 5 cubed plus 3 cubed = 13 + 125+ 27″)it always equals 153. How amazing is that?
- That’s not all either…153 is an odd number—which basically means it isn’t divisible by 2… so after dividing this number in half you’ll still have a whole piece to spare! And even better news–153 reverses into 351 which makes it what they call an ‘Emirp’—a particular type of prime where reversing its digits creates yet another prime number. Lastly, both Lucas Numbers and Harshad Numbers recognize 153 as being part of their club too–making our friend “Prime-Number-153” quite popular indeed.

## Examples of Factor of 153

**1) What is the greatest common factor between 70 and 153?**

**Answer: **The greatest common factor between 70 and 153 is 1.

**2) Find four consecutive multiples of seven that add up to 153.****Answer:** The four consecutive multiples of seven that add up to 153 are 7, 14, 21, and 28 (7 + 14 + 21 + 28 = 91).

**3) What two numbers multiplied together equal 153?**

**Answer: **The two numbers which multiplied together equal 153 are 9 and 17 (9 × 17 = 153).

**4) Divide 153 by its largest factor to find its smallest factor. ****Answer: **Divide 153 by its largest factor which is 17 to find its smallest factor; the answer is 9.

**5) If a store sold a product for $153 before tax, how much would it cost with 8% tax added? ****Answer: **With 8% tax added the product would cost 165.44 dollars ($153 + ($153 x 0.08)= 165.44).

**6) What are the factors of 153?****Answer: **The factors of 153 are 1, 3, 9, 17, 51, and 153.

**7) How many prime numbers are factors of 152?****Answer: **Three prime numbers – 3, 17, and 51 – are factors of 153.

**8) Find three consecutive even integers whose sum equals 153.****Answer: **The three consecutive even integers whose sum equals 153 are 74 , 76 , and 78 (74 + 76 + 78= 228).

**9) Find two consecutive odd numbers whose product is equal to 154.****Answer: **The two consecutive odd numbers whose product is equal to 154 are 17 and 19 (17 × 19 = 323).

**10) Rachel purchased 5 items at a store for $31 each plus tax at 8%. How much did she spend with tax included?Answer: **With tax included Rachel spent 167.28 dollars ((5×31)+((5×31)* 0.08)= 167.28).

**Looking to Learn Math? Explore Wiingy’s Online Math Tutoring Services to learn from top mathematicians and experts.**

## Frequently Asked Questions on Factors of 153

**What is the greatest common factor between 70 and 153?**

The greatest common factor between 70 and 153 is 1.

**Find four consecutive multiples of seven that add up to 153.**

The four consecutive multiples of seven that add up to 153 are 7, 14, 21, and 28 (7 + 14 + 21 + 28 = 91).

**What two numbers multiplied together equal 153?**

The two numbers that when multiplied together equal 153 are9 and 17 (9 × 17 = 153).

**Divide 153 by its largest factor to find its smallest factor.**

Divide 153 by its largest factor which is17to find its smallest factor; the answer is 9.

**If a store sold a product for $153 before tax, how much would it cost with 8% tax added?**

With 8% tax added the product would cost 165.44 dollars ($153 + ($153 x 0.08)= 165.44).

**What are the factors of 153?**

The factors of 153 are 1, 3, 9, 17, 51, and 153.

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

Three prime numbers – 3, 17, and 51 – are factors of 153.

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

The three consecutive even integers whose sum equals 153 are 74, 76, and 78 (74 + 76 + 78= 228).

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

**154.**

The two consecutive odd numbers whose product is equal to 154 are 17 and 19 (17 × 19 = 323).

**Rachel purchased 5 items at a store for $31 each plus tax at 8%. How much did she spend with tax included?**

With tax included Rachel spent 167.28 dollars ((5×31)+((5×31)* 0.08)=167.28).

Written by

Prerit Jain