Factors of 150 Using Prime Factorization
Introduction
The integers that can divide the 150 exactly are known as factors of 150. There are twelve factors in total for 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
Deriving Factor List for 150
We use divisibility rules of numbers and division facts to derive the factor list of 150.
Divisor | Is the number a factor of 150? | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of every number. | 1 \( \times \) 150 = 150 |
2 | Yes, 150 is even. | 2 \( \times \) 75 = 150 |
3 | Yes, 1 + 5 + 0 = 6 is divisible by 3. | 3 \( \times \) 50 = 150 |
4 | No, 150 \( \div \) 4 = 37 R2 | - |
5 | Yes, the ones digit is 0. | 5 \( \times \) 30 = 150 |
6 | Yes, 150 is even and is divisible by 3. | 6 \( \times \) 25 = 150 |
7 | No, 150 \( \div \) 7 = 21 R3 | - |
8 | No, 150 \( \div \) 8 = 18 R6 | - |
9 | Yes, 1 + 5 + 0 = 6 is not divisible by 9. | - |
10 | Yes, the ones digit is 0. | 10 \( \times \) 15 = 150 |
11 | No, 150 \( \div \) 11 = 13 R7 | - |
12 | No, 150 \( \div \) 12 = 12 R6 | - |
13 | No, 150 \( \div \) 13 = 11 R7 | - |
14 | No, 150 \( \div \) 14 = 10 R10 | - |
15 | Yes, 150 \( \div \) 15 = 10 R0 | 15 \( \times \) 10 = 150 |
Therefore, the factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
Prime Factorization of 150
The factor tree of 150 that shows us the prime factors of 150 can be written in the following manner.
Factor Tree of 150
The prime factorization of 150 is \( 2~\times~3~\times~5^2 \), which means that 2, 3 and 5 are the prime factors of 150.
Read More:
Positive Factor Pairs of 150
Factor pairs or pair factors of 150 are two factors of 150, which when multiplied together produce 150.
Solved Factors of 150 Examples
Example 1: Find the common factors of 150 and 108
Solution:
The common factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
The common factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108.
Hence, the common factors of 150 and 108 are 1, 2, 3 and 6
Example 2: Find the common factors of 150 and 90.
Solution:
The common factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
The common factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Hence, the common factors of 150 and 90 are 1, 2, 3, 5, 6, 10, 15 and 30.
Example 3: Jake loves animals. He has tarantulas and birds. If the total number of legs of all animals is 150 and we know that the maximum number of legs belong to tarantulas, how many birds does Jake have?
Solution:
Total number of legs = 150
A tarantula has 8 legs and a bird has 2 legs.
We know that the maximum number of legs belong to tarantulas. So,
\( \frac{150}{8} \) = 18 R6. When 150 is divided by 8, we get the quotient as 18 and the remainder as 6. So there are 18 tarantulas.
But there are 6 legs remaining.
Therefore, \( \frac{6}{2} \) = 3 which means that there are 3 birds.
So in total Jake has 18 tarantulas and 3 birds.
1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75 and 150 are the factors of 150.
2\( \times \) 3 \( \times \) 5 \( \times \) 5 = 2 \( \times \) 3 \( \times \) \( 5^2 \) is the prime factorization of 150.
(1, 150), (2, 75), (3, 50), (5, 30), (6, 25) and (10, 15) are the positive pair factors of 150.
Yes, 25 is a factor of 150. As 25 divides 150 exactly and leaves the remainder 0.