Factors

# Factors of 180 | Prime Factorization of 180 | Factor Tree of 180

Written by Prerit Jain

Updated on: 18 Aug 2023

Contents

### Factors of 180 | Prime Factorization of 180 | Factor Tree of 180

Factors of 180 | Factor Pairs of 180 | Prime factors of 180 |
---|---|---|

180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. | (1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), (10, 18) and (12, 15) | 180=2 × 2 × 3 × 3 × 5 |

Calculate Factors of

**The Factors are**

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

**What are the factors of 180**

180 has lots of factors, which are the numbers that you can use to divide it. To find these factors; First, let’s try dividing 180 by every whole number less than itself and greater than zero (1-179). Anytime there’s no remainder left over then whatever number was used in the division has become a factor for 180! Coming to its prime factorization – if we break down each factor into only those “prime” or smallest possible parts such as 3 x 2 x 5 = 30 – the process will be much quicker. We have found all 1,2,3.,4…90 –the twelve different ways that 180 can be divided evenly–in just minutes!

**How to Find Factors of 180**

Four different methods to find the factors of 180:

The factor of 180 using Multiplication Method

Factors of 180 using the Division Method

Prime Factorization of 180

Factor tree of 180

**Factors of 180 using Multiplication Method**

All the ways two numbers can multiply together and make 180, First of all, let’s think about multiplying really small numbers like 1×180 or 2×90 which equals 180. Proceed to 45 x 4 = 180; 30 X 6 is also equal to 180. And lastly, for bigger groupings: 18 x 10 and 9 times 20 each give an answer 180 again!

**Factors of 180 Using Division Method**

Finding factors of numbers using the division method involves the following steps Take the number 180. Start by dividing it by 2, then 3, and so on until there are no more numbers that can divide into it evenly with no remainder left over. In this case, our factors turn out to be 2,3,5,6,9,10,15, 30 45 90, and 180.

**Prime Factorization of 180**

Calculate Prime Factors of

The Prime Factors of 180 =

2 x

2 x

3 x

3 x

5

A number can be split into its prime parts, like an equation known as Prime Factorization. For 180 start by dividing it by the smallest possible prime number: 2. We do that and get 90 which is not a prime number so divide 90 by 2 again and now have 45; Let’s keep going dividing 45 further by 3 gives us 15 take 15 once more and divide it fully through another 3 which brings us back around to 5 finally being all primes numbers making up this sequence.

(180 = 2 x2 x 3×3 X5).

**Factor tree of 180**

A factor tree is used to break down a number into its prime factors. To demonstrate how this works, let’s create one for 180!

First, we start at the top of our “tree” with the number 180 and then we search for numbers and divide it evenly (without remainders). In this case, it’s 2 so write 90 below that line connecting them both together.

Write 90 again and find out which smallest prime divides the number without leaving anything over -which would be two again.

Write 45 under your first results line connected by another branch like before.

Go on till there are no more divisions possible but only Prime Numbers as leaves from your now complete Factor Tree: 2x2x3x5=180

**Factor Pairs of 180**

Calculate Pair Factors of

1 x 180=180

2 x 90=180

3 x 60=180

4 x 45=180

5 x 36=180

6 x 30=180

9 x 20=180

10 x 18=180

12 x 15=180

15 x 12=180

18 x 10=180

20 x 9=180

30 x 6=180

36 x 5=180

45 x 4=180

60 x 3=180

90 x 2=180

So Pair Factors of 180 are

(1,180)

(2,90)

(3,60)

(4,45)

(5,36)

(6,30)

(9,20)

(10,18)

(12,15)

(15,12)

(18,10)

(20,9)

(30,6)

(36,5)

(45,4)

(60,3)

(90,2)

Factor pairs are nothing but if you have a bigger number and break it down to pair factors their product will also be the same bigger number; just two numbers multiplied together to get the same answer.

Step 1: Make a list of every single number divided into 180 evenly which is 1, 2, 87, and 180 itself.

Step 2:Then take each one in turn and figure out what would be needed to multiply by it to give us the original 180 again (divide by factors).

For example, if we start with 180 tries dividing this down twice using its prime factors 2 & 3 will result in 29 which means our pair must consist of both 87 &2 as when multiplied they should result in 180. So there’s 1 set complete – (1,173) but now keep going until all 4 options are accounted for – giving us another possible factor pair being found from dividing up 153 once more using 5&3 resulting in 31…which combined other valid Factor Pair :(5,31 ) Thereby completing all factor pairs associated specifically with 180.

**Factors of 180 – Quick Recap**

**Factors of 180:** 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.

**Negative Factors of 180:** -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -30, -36, -45, -60, -90, and -180.

**Prime Factors of 180:** 2 × 2 × 3 × 3 × 5

**Prime Factorization of 180:** 2 × 2 × 3 × 3 × 5

**Fun Facts of Factors of 180**

Being an even number, which means 180 can be evenly divided by two. But 180 has more factors than just 2; there are 12 different factors that you multiply together to get a total of 180! The list includes 1 and all the prime numbers up to 90 (2, 3,4,5,6 9 10 15 18 30 45).

180 is special with its unique factor combination – the sum of all factors together (except for 180 ), they equal 144. And when we multiply them the result is 3 million 636 thousand 800! That’s why we call this kind of number highly composite as it has many divisors or parts.

On top of that, did you know that every multiple of nine will have digits adding up to nine too asm20 x9 =180…all the individual digits on their own add up to make 9 as well!

**Examples of Factor of 180**

1. Martha has 180 apples that she wants to divide among her daughter and two friends evenly. How many apples will each person get?

Answer: Each person will get 60 apples (180 ÷ 3 = 60).

2. If the number 180 is multiplied by 8, what is the result?

Answer: The result is 1,440 (180 x 8 = 1,440).

3. What are the biggest prime factors of 180?

Answer: The biggest prime factor of 180 is 30.

4. Express 180 as a product of two consecutive numbers.

Answer: 12 x 15=180

5. What is the sum of all factors of 180?

Answer: The sum of all factors of 180 is 252 (1 + 2 + 3 + 5 + 6 + 10 + 30 = 252).

6. Find two factors whose difference is 88 when multiplied by 6 and 18 respectively?

Answer: 6 and 24 are the two numbers that have a difference of 88 when multiplied by 6 and 18 respectively (6 x 6 = 36 and 24 x 18 = 432 – 36 = 396).

7. Is there any square root of 180 that is an integer?

Answer: No, there is no square root of 180 that is an integer because the square root must always be an irrational number when dealing with non-perfect squares such as

180.

8. What are all the even factors of 180?

Answer: All the even factors of 180 are 2, 6, 10, 30, and 60.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

**Frequently Asked Questions**

### What is the prime factorization of 180?

The prime factorization of 180 is 2 x 3 x 3 x5.

### How many factors does 180 have?

180 has seven distinct factors (1, 2, 3, 5, 6, 10, and 30).

### Is 180 a composite number?

Yes, 180 is a composite number.

### What is the sum of all factors of 180?

The sum of all factors of 180 is 252 (1 + 2 + 3 + 5 + 6 + 10 + 30 = 252).

### Is the number 180 divisible by 4?

Yes, 180 is divisible by 4 (180 ÷ 4 = 45).

### Does 180 have any odd factors?

Yes, 180 has five odd factors (3,5,9,15,45).

### What is the largest prime factor of 180?

The largest prime factor of 180 is 30.

### Can you express 180 as a product of two consecutive numbers?

Yes – 12 x 15 =180

### Can you find two consecutive even integers whose product equals 180?

No, there are no consecutive even integers whose product equals 180

### Is there any square root of 180 that is an integer?

No, there is no square root of 180 that is an integer because the square root must always be an irrational number when dealing with non-perfect squares such as 176

Written by by

Prerit Jain