The factors of 72 are the numbers that completely divide 72 with the remainder zero. Thus we can say that the factors of 72 are the divisors of 72. In this section, we will learn about the factors of 72 and the prime factors of 72.
Also Read:
- Basic concepts of factors
- Square root of 72
Table of Contents
Highlights of Factors of 72
- 72 = 2×2×2×3×3 = 23×32 is the prime factorization of 72.
- The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
- 2 and 3 are the prime factors of 72.
- The negative factors of 72 are –1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, and –72.
What are the Factors of 72?
To find the factors of 72, we need to write the number 72 multiplicatively in all possible ways. Note that we can write 72 multiplicatively as follows:
72 = 1×72
72 = 2×36
72 = 3×24
72 = 4×18
72 = 6×12
72 = 8×9
As there are no other ways we can express 72 multiplicatively, we will stop now. Hence the factors of 72 in pairs are given as follows:
| 72 = a×b | Factors in Pairs (a,b) |
| 72 = 1×72 | (1, 72) |
| 72 = 2×36 | (2, 36) |
| 72 = 3×24 | (3, 24) |
| 72 = 4×18 | (4, 18) |
| 72 = 6×12 | (6, 12) |
| 72 = 8×9 | (8, 9) |
Thus the pair factors of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9). Since all the numbers appearing in pair factors are the factors of 72, we conclude that the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Number of Factors of 72
The total number of factors of 72 is twelve.
Prime Factors of 72
We have found above that the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Among those factors, we observe that only 2 and 3 are prime numbers as they do not have any proper divisors.
∴ The prime factors of 72 are 2 and 3.
How to Find Factors of 72?
By division method, we will determine the factors of 72. In this method, we will find the numbers that can divide 72 completely with the remainder zero. See that
72/1=72 and the remainder is 0.
∴ 1 and 72 are factors of 72.
72/2=36 and the remainder is 0.
∴ 2 and 36 are factors of 72.
72/3=24 and the remainder is 0.
∴ 3 and 24 are factors of 72.
72/4=18 and the remainder is 0.
∴ 4 and 18 are factors of 72.
72/6=12 and the remainder is 0.
∴ 6 and 12 are factors of 72.
72/8=9 and the remainder is 0.
∴ 8 and 9 are factors of 72.
Note that no numbers other than the numbers in violet color can divide 72. So the numbers in violet color, that is, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 are the complete list of factors of 72.
FAQs on Factors of 72
Answer: The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Answer: As 72/6=12, the number 6 is a factor of 72.
