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Factor Pairs of 72
All Factor Pairs of 72
Here are all the factor pairs of 72:
(1, 72)
(2, 36)
(3, 24)
(4, 18)
(6, 12)
(8, 9)
Total: 6 factor pairs
Visual Representation of Factors
These are all the factors of 72:
1
2
3
4
6
8
9
12
18
24
36
72
Properties of 72
Number Type
Abundant Number
Sum of All Factors
195
Sum of Proper Divisors
123
Total Factors
12
Prime Factorization
23 × 32
Perfect Square?
No
How to Calculate Factor Pairs of 72
Step-by-Step Process
To find all factor pairs of 72, we need to identify all integers that divide 72 evenly (with no remainder).
- Start with the smallest factor, which is always 1
- Check each integer from 1 up to the square root of 72 (v72 ≈ 8.49)
- For each factor found, its corresponding pair is calculated by dividing 72 by that factor
Calculation Example
Let's work through finding the factor pairs of 72:
| Factor Check | Division | Result | Factor Pair |
|---|---|---|---|
| 72 ÷ 1 | 72.00 | Integer result | (1, 72) |
| 72 ÷ 2 | 36.00 | Integer result | (2, 36) |
| 72 ÷ 3 | 24.00 | Integer result | (3, 24) |
| 72 ÷ 4 | 18.00 | Integer result | (4, 18) |
| 72 ÷ 5 | 14.40 | Not a divisor | - |
| 72 ÷ 6 | 12.00 | Integer result | (6, 12) |
| 72 ÷ 7 | 10.29 | Not a divisor | - |
| 72 ÷ 8 | 9.00 | Integer result | (8, 9) |
Explore More Factor Pairs
Check out factor pairs of these randomly selected numbers:
| Number | Factor Pairs | Total Pairs | Details |
|---|---|---|---|
| 8 | (1, 8), (2, 4) | 2 | View Details |
| 12 | (1, 12), (2, 6), (3, 4) | 3 | View Details |
| 18 | (1, 18), (2, 9), (3, 6) | 3 | View Details |
| 28 | (1, 28), (2, 14), (4, 7) | 3 | View Details |
| 45 | (1, 45), (3, 15), (5, 9) | 3 | View Details |
| 100 | (1, 100), (2, 50), (4, 25), (5, 20), (10, 10) | 5 | View Details |
This table refreshes with new examples each time you visit.
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More About Abundant Numbers
Abundant Numbers
An abundant number is a positive integer for which the sum of its proper divisors is greater than the number itself. The number 72 is abundant because the sum of its proper divisors (123) exceeds 72.
The smallest abundant number is 12, whose proper divisors are 1, 2, 3, 4, and 6, which sum to 16.