Factors of 60
Factors | Factor Pairs | Prime factors |
|---|---|---|
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | (1,60), (2,30), (3,20), (4,15), (5,12), (6,10) | 36 = 2 × 2 × 3 × 5 |
What are the factors of 60?
The factors of 60 are integers that divide 60 without leaving any remainder, or in other words, the factors of 60 divide 60 evenly.
Example: 5 is a factor of 60 because when we divide 60 by 5, it gives us 12 as the quotient and 0 as the remainder. Here, the quotient 12 is also a factor of 60.
So, to check if any number is a factor of 60 or not, divide 60 by that number and verify whether the remainder is zero or not.
Factor list of 60
The factors of 60 can be obtained by applying the divisibility rules and division facts.
Number | Is the number a factor of 60? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 × 60 = 60 |
2 | Yes, 60 is even. | 2 × 30 = 60 |
3 | Yes, 6 + 0 = 6 is divisible by 3 | 3 × 20 = 60 |
4 | Yes, 60 \(\div\) 4 = 15 Remainder = 0 | 4 × 15 = 60 |
5 | Yes, 60 \(\div\) 5 = 12 Remainder = 0 | 5 × 12 = 60 |
6 | Yes, 60 is even and divisible by 3 | 6 × 10 = 60 |
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Prime Factors of 60
A factor tree can be used to learn about the prime factorization of 60.
From the factor tree, we can see that the prime factorization of 60 is 2 × 2 × 3 × 5 = \(2^2\)× 3 × 5.
This means 2, 3 and 5 are the prime factors of 60.
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Factor pairs of 60
The factor pair of 60 is the combination of two factors of 60, which when multiplied together, result in 60.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Example: (2, 30) is the factor pair of 60.
The factor pair can be a positive pair or a negative pair.
Positive Factor Pairs of 60
Positive factor of 60 | Positive Factor Pairs of 60 |
|---|---|
1 × 60 | (1, 60) |
2 × 30 | (2, 30) |
3 × 20 | (3, 20) |
4 × 15 | (4, 15) |
5 × 12 | (5, 12) |
6 × 10 | (6, 10) |
Rapid recall
Solved Factors of 60 Examples
Example 1: Find the common factors of 55 and 60.
Solution:
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Factors of 55: 1, 5, and 11.
So, the common factors of 55 and 60 are 1 and 5.
Example 2: How many factors does 60 have?
Solution:
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
So, there are 12 factors of 60.
Example 3: Find the product of all the prime factors of 60.
Solution:
Prime factors of 60 are 2, 3, and 5.
Product of prime factors = 2 × 3 × 5
= 30.
So, the product of all the prime factors of 60 is 30.
Example 4:
A school library has a collection of 60 books on the history of America. The books are to be arranged evenly on 15 shelves. How many books will be placed on each shelf?
Solution:
60 books are to be evenly arranged on 15 shelves.
To find out how many books can be placed on each shelf, we will divide 60 by 15, that is, \(\frac{60}{15}\)
= \(\frac{15\times4}{15}\) [(15, 4) is a factor pair of 60]
= 4 [Divide both the numerator and the denominator by 15]
As a result, 4 books can be placed on one shelf.
No, when you divide 60 by 9, it will give 6 as a remainder, that is, 9 does not divide 60 evenly.
Numbers that divide 60 evenly, that is, leave zero as the remainder, are known as factors of 60.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Hence, the sum of all the factors of 60 is
= 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 + 60 = 168
Hence, the sum is 168.
Yes, 60 is a composite number as it has factors other than one and itself. It has the factors 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 other than 1 and 60.
The factors of 36 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
So, the least factor of 60 is 1 and the greatest factor is 60 itself.