Factors of 150
Factors of 150 are the whole numbers, that divide the original number into equal parts. The factors of 150 will divide it evenly. These factors cannot be a fraction or decimal number. There is a total of 12 factors of 150. They are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. The sum of all the factors of 150 is 372.
The pair 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 are 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 that could be either positive or negative but not a fraction or decimal number.
What are the Factors of 150?
The factors of 150 are the numbers that divide 150 exactly without leaving any remainder. As the number 150 is an even composite number, 150 has many factors other than 1 and 150. Thus, the factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
How to Find Factors of 150?
There are two methods to find the factors of 150:
- Division method
- Prime factorisation of 150
Factors of 150 by Division Method
In this method, we will perform the simple arithmetic division method. As we can see, 150 is an even number, thus it is divisible by 2. Hence, 2 is a factor of 150. Now let us check, by how many numbers, 150 is evenly divisible.
- 150/1 = 150; 1 is a factor of 150
- 150/2 = 75; 2 is a factor of 150
- 150/3 = 50; 3 is a factor of 150
- 150/5 = 30; 5 is a factor of 150
- 150/6 = 25; 6 is a factor of 150
- 150/10 = 15; 10 is a factor of 150
- 150/15 = 10; 15 is a factor of 150
- 150/25 = 6; 25 is a factor of 150
- 150/30 = 5; 30 is a factor of 150
- 150/50 = 3; 50 is a factor of 150
- 150/75 = 2; 75 is a factor of 150
- 150/150 = 1; 150 is a factor of 150
Therefore, the factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75 and 150.
Prime Factorisation of 150
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 number, say 2.
150 ÷ 2 = 75
Step 2: You will get a fractional number if you divide 75 by 2. Continue with the next prime number, say 3.
75 ÷ 3 = 25
Step 3: Again you will get a fractional value when you divide 25 by 3 hence, 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 5^{2}, 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 factorization. The prime factor representation of 150 is 2 x 3 x 5^{2}. The exponents in the prime factorization 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.
Factor Tree of 150
Pair Factors of 150
Pair factors of 150 are the integers that are multiplied together to get the original number. 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:
Positive Factors of 150 |
Positive Pair Factors of 150 |
1 × 150 |
(1, 150) |
2 × 75 |
(2, 75) |
3 × 50 |
(3, 50) |
5 × 30 |
(5, 30) |
6 × 25 |
(6, 25) |
10 × 15 | (10, 15) |
Therefore, the positive pair factors of 150 are (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), and (10, 15).
Negative Factors of 150 |
Negative Pair Factors of 150 |
-1 × -150 |
(-1, -150) |
-2 × -75 |
(-2, -75) |
-3 × -50 |
(-3, -50) |
-5 × -30 |
(-5, -30) |
-6 × -25 |
(-6, -25) |
-10 × -15 |
(-10, -15) |
Therefore, the negative pair factors of 150 are (-1, -150), (-2, -75), (-3, -50), (-5, -30), (-6, -25), and (-10, -15).
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Solved Examples on Factors of 150
Example 1:
Find the common factors of 150 and 151.
Solution:
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
The factors of 151 are 1 and 151.
As the number 151 is a prime number, the common factor of 150 and 151 is 1.
Example 2:
Find the common factors of 150 and 149.
Solution:
Factors of 150 = 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
Factors of 149 = 1 and 149.
Therefore, the common factor of 150 and 149 is 1, as 149 is a prime number.
Example 3:
Find the common factors of 150 and 125.
Solution:
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
The factors of 125 are 1, 5, 25, 125.
Therefore, the common factors of 150 and 125 are 1, 5 and 25.
Practice Questions on Factors of 150
- Find if 4 is a factor of 150. Give reason.
- How many factors of 150 are even numbers?
- What is the sum of prime factors of 150?
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Frequently Asked Questions on Factors of 150
What are the factors of 150?
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
What is the prime factorization of 150?
The prime factorization of 150 is 2 x 3 x 5 x 5 or 2 x 3 x 5^{2}.
What are the positive pair factors of 150?
The positive pair factors of 150 are (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), and (10, 15).
What are the negative pair factors of 150?
The negative pair factors of 150 are (-1, -150), (-2, -75), (-3, -50), (-5, -30), (-6, -25), and (-10, -15).
Is 25 a factor of 150?
Yes, 25 is a factor of 150. As the number 25 divides 150 exactly without leaving a remainder, 25 is a factor of 150.
What is the sum of all factors of 150?
1 + 2 + 3 + 5 + 6 + 10 + 15 + 25 + 30 + 50 + 75 + 150 = 372