 # Factors of 150

The factors of 150 are the numbers, that produce the result as 150 when two numbers are multiplied together. Consider an example, the factor pairs of 47 is written as (1, 47) and (-1,-47). When we multiply the pair of negative factors, the result should give the original number, such as multiplying -1 × -47 then we get the number 47. Thus, we can consider both positive and negative factor pairs of 47. Factor pairs of the number 150 are the whole numbers which could be either positive or negative but not a fraction or decimal number. To find the factors of a number, 150, we will use the factorization method.

In the factorization method, first take the numbers, 1 and 150 as factors of 150 and proceed with finding the other pair of multiples of 150 which gives the results as an original number. To understand this method in a better way, read the article below to find factor 150 in pairs and also the division method to find the prime factors of 150 is discussed.

## Pair Factors of 150

To find the pair factors of 150, multiply the two numbers in a pair to get the original number as 150, such numbers are as follows

If 1 × 150 = 150, then (1, 150) is a pair factor of 150.

Similarly,

2 × 75 = 150, (2, 75) is a pair factor of 150

3 × 50 = 150, (3, 50) is a pair factor of 150

5 × 30 = 150, (5, 30) is a pair factor of 150

6 × 25 = 150, (6, 25) is a pair factor of 150

10 × 15 = 150, (10, 15) is a pair factor of 150

Therefore, the positive pair factors of 150 are (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), and (10, 15).

To find the negative pair factors of 150, then proceed with the following steps

If -1 × -150 = 150, then (-1, -150) is a pair factor of 150.

Similarly,

-2 × -75 = 150, (-2, -75) is a pair factor of 150

-3 × -50 = 150, (-3, -50) is a pair factor of 150

-5 × -30 = 150, (-5, -30) is a pair factor of 150

-6 × -25 = 150, (-6, -25) is a pair factor of 150

-10 × -15 = 150, (-10, -15) is a pair factor of 150

Therefore, the negative pair factors of 150 are (-1, -150), (-2, -75), (-3, -50), (-5, -30), (-6, -25), and (-10, -15).

### How to calculate the Factors of 150?

Learn the following steps to calculate the factors of 150.

• First, write the number 150
• Find the two numbers, which gives the result as 150 under the multiplication, say 2 and 75, such as 2 × 75 = 150.
• We know that 2 is a prime number has only two factors, i.e., 1 and the number itself (1 and 2) which cannot be further factorized.
• 2 = 2 × 1

• But look at the number 75, which is a composite number but not a prime number and it can be further factorized.
• 75 can be factored as 5 x 5 x 3 x 1

• Therefore, the factorization of 150 is written as 150 = 1 x 2 x 3 x 5 x 5

Finally, write down all the unique numbers that are obtained as factors.

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

### Prime Factors of 150 By Division Method

The number 150 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 150.

Step 1: The first step is to divide the number 150 with the smallest prime factor, say 2.

150 ÷ 2 = 75

Step 2: You will get a fractional number if you divide 75 by 2. So continue with the next prime factor, say 3.

75 ÷ 3 = 25

Step 3: Again you will get a fractional value when you divide 25 by 3 and continue with the next prime number say 5.

25 ÷ 5 = 5

5 ÷ 5 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 150 are written as 2 x 3 x 5 x 5 or 2 x 3 x 52, where 2, 3 and 5 are the prime numbers.

It is possible to find the exact number of factors of a number 150 with the help of prime factorisation. The prime factor of the 150 is 2 x 3 x 52. The exponents in the prime factorisation are 1, 1 and 2. Add the number 1 with the exponents and multiply it. (1+1)(1+1)(2+1) =2 x 2 x 3= 12. Therefore, the number 150 has 12 factors.

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