# Factors of 150

Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150

#### How to find factors of a number

 1.   Find factors of 150 using Division Method 2.   Find factors of 150 using Prime Factorization 3.   Find factors of 150 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 150

• Divide 150 by 1: 150 ÷ 1 : Remainder = 0
• Divide 150 by 2: 150 ÷ 2 : Remainder = 0
• Divide 150 by 3: 150 ÷ 3 : Remainder = 0
• Divide 150 by 5: 150 ÷ 5 : Remainder = 0
• Divide 150 by 6: 150 ÷ 6 : Remainder = 0
• Divide 150 by 10: 150 ÷ 10 : Remainder = 0
• Divide 150 by 15: 150 ÷ 15 : Remainder = 0
• Divide 150 by 25: 150 ÷ 25 : Remainder = 0
• Divide 150 by 30: 150 ÷ 30 : Remainder = 0
• Divide 150 by 50: 150 ÷ 50 : Remainder = 0
• Divide 150 by 75: 150 ÷ 75 : Remainder = 0
• Divide 150 by 150: 150 ÷ 150 : Remainder = 0

Hence, Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150

#### 2. Steps to find factors of 150 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 150 using the division method, follow these steps:

• Step 1. Start dividing 150 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 150, which is 2. Divide 150 by 2 to obtain the quotient (75).
150 ÷ 2 = 75
• Step 3. Repeat step 1 with the obtained quotient (75).
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 150 is, 150 = 2 x 3 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 150 as shown below:

So, the prime factorization of 150 is, 150 = 2 x 3 x 5 x 5.

#### 3. Find factors of 150 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 150 would be the two numbers which, when multiplied, give 150 as the result.

The following table represents the calculation of factors of 150 in pairs:

Factor Pair Pair Factorization
1 and 150 1 x 150 = 150
2 and 75 2 x 75 = 150
3 and 50 3 x 50 = 150
5 and 30 5 x 30 = 150
6 and 25 6 x 25 = 150
10 and 15 10 x 15 = 150

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 150. They are called negative pair factors.

Hence, the negative pairs of 150 would be ( -1 , -150 ) , ( -2 , -75 ) , ( -3 , -50 ) , ( -5 , -30 ) , ( -6 , -25 ) and ( -10 , -15 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 150 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 are exact divisors of 150.
• 1 is a factor of every number. Eg. 1 is a factor of 150.
• Every number is a factor of zero (0), since 150 x 0 = 0.

• How do you find factors of a negative number? ( eg. -150 )?

Factors of -150 are -1, -2, -3, -5, -6, -10, -15, -25, -30, -50, -75, -150.

• What is the sum of all factors of 150?

The sum of all factors of 150 is 372.

• What is prime factorization of 150?

Prime factorization of 150 is 2 x 3 x 5 x 5.

• What are the pair factors of 150?

Pair factors of 150 are (1,150), (2,75), (3,50), (5,30), (6,25), (10,15).

• What are six multiples of 150?

First five multiples of 150 are 300, 450, 600, 750, 900, 1050.

• Is 150 a whole number?

Yes 150 is a whole number.

• Which is the smallest prime factor of 150?

Smallest prime factor of 150 is 2.

• What are five multiples of 150?

First five multiples of 150 are 300, 450, 600, 750, 900.

• Write all factors of 150?

Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.

#### Examples of Factors

Joey wants to write all the prime factors of 150 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 150 are 2, 3, 5, 5.
So in exponential form it can be written as 2 x 3 x 52.

How many factors are there for 150?

Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 150. Can you predict the answer?

11 factor(s) of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75.

Sammy is puzzled while calculating the prime factors of 150. Can you help him find them?

Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.
Prime factors of 150 are 2, 3, 5, 5

What is prime factorization of 150?

Prime factorization of 150 is 2 x 3 x 5 x 5 = 2 x 3 x 52.

Ariel has been assigned the task to find the product of all the prime factors of 150. Can you help her?

Prime factors of 150 are 2, 3, 5, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 150?

Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.
Even factors of 150 are 2, 6, 10, 30, 50, 150.
Hence, product of even factors of 150 is; 2 x 6 x 10 x 30 x 50 x 150 = 27000000.