Factors of 72
What are the Factors of 72?
Numbers that divide 72 without leaving any remainder are known as factors of 72.
For Example: 9 is a factor of 72 because when we divide 72 by 9 it results in the quotient as 8 and the remainder as 0. The quotient is also a factor of 72.
Thus, to check if a number is a factor of 72 or not, divide 72 by that number, if the remainder is zero, then that number is said to be a factor of 72.
Factor list of 72
Therefore the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Prime Factors of 72
The number 72 is a composite number, that is, it has more than two numbers as factors. To carry out prime factorization of 72, we will keep dividing 72 by its prime factors, until we get the result as 1.
As 72 is even, let’s start dividing by 2.
72 ÷ 2 = 36
Continue the division process by 2;
36 ÷ 2 = 18
18 ÷ 2 = 9
Now, divide it by the next prime number, that is, 3.
9 ÷ 3 = 3
3 ÷ 3 = 1
So, the prime factorization of 72 = 2 × 2 × 2 × 3 × 3
= 2\( ^3\) × 3\( ^2\)
This means that 2 and 3 are the only prime factors of 72.
Hence the Factor Tree of 72 can be written as:
Factor pairs of 72
Factor pairs of 72 are two factors of 72 that when multiplied together give the product as 72.
Hence, the positive pair factors of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12) and (8, 9)
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Solved Examples
Example 1: Find the factors common between 72 and 30.
Solution:
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72
Factors of 30 = 1, 2, 3, 5, 6, 10, 15 and 30
Therefore, the factors common between 72 and 30 are 1, 2, 3 and 6.
Example 2: Find the factors common between 45 and 72.
Solution:
Factors of 45 = 1, 3, 5, 9, 15, 45
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72
Therefore, the factors common between 45 and 72 are 1, 3 and 9.
Example 3: Penelope decides to divide 72 toffees among 7 of her friends. How can she divide the toffees equally?
Solution:
\(72\div~7=10R2 \). As 7 is not a factor of 72, we get a remainder here of 2.
Therefore, to divide the toffees equally, Penelope would have to give each of her 7 friends 10 toffees each but she would be left with 2 toffees.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
So, the least factor of 72 is 1 and the greatest factor is 72 itself.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Sum of factors = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 + 72 = 195
So, the sum of factors of 72 is 195.
Yes, 18 is a factor of 72. As 18 divides 72 exactly without leaving any remainder.
The prime factorization of 72 is 2×2×2×3×3 or 2\( ^3\) × 3\( ^2 \).