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Factor Pairs of 126
All Factor Pairs of 126
Here are all the factor pairs of 126:
(1, 126)
(2, 63)
(3, 42)
(6, 21)
(7, 18)
(9, 14)
Total: 6 factor pairs
Visual Representation of Factors
These are all the factors of 126:
1
2
3
6
7
9
14
18
21
42
63
126
Properties of 126
Number Type
Abundant Number
Sum of All Factors
312
Sum of Proper Divisors
186
Total Factors
12
Prime Factorization
2 × 32 × 7
Perfect Square?
No
How to Calculate Factor Pairs of 126
Step-by-Step Process
To find all factor pairs of 126, we need to identify all integers that divide 126 evenly (with no remainder).
- Start with the smallest factor, which is always 1
- Check each integer from 1 up to the square root of 126 (v126 ≈ 11.22)
- For each factor found, its corresponding pair is calculated by dividing 126 by that factor
Calculation Example
Let's work through finding the factor pairs of 126:
| Factor Check | Division | Result | Factor Pair |
|---|---|---|---|
| 126 ÷ 1 | 126.00 | Integer result | (1, 126) |
| 126 ÷ 2 | 63.00 | Integer result | (2, 63) |
| 126 ÷ 3 | 42.00 | Integer result | (3, 42) |
| 126 ÷ 4 | 31.50 | Not a divisor | - |
| 126 ÷ 5 | 25.20 | Not a divisor | - |
| 126 ÷ 6 | 21.00 | Integer result | (6, 21) |
| 126 ÷ 7 | 18.00 | Integer result | (7, 18) |
| 126 ÷ 8 | 15.75 | Not a divisor | - |
| 126 ÷ 9 | 14.00 | Integer result | (9, 14) |
| 126 ÷ 10 | 12.60 | Not a divisor | - |
| 126 ÷ 11 | 11.45 | Not a divisor | - |
Explore More Factor Pairs
Check out factor pairs of these randomly selected numbers:
| Number | Factor Pairs | Total Pairs | Details |
|---|---|---|---|
| 6 | (1, 6), (2, 3) | 2 | View Details |
| 12 | (1, 12), (2, 6), (3, 4) | 3 | View Details |
| 14 | (1, 14), (2, 7) | 2 | View Details |
| 24 | (1, 24), (2, 12), (3, 8), (4, 6) | 4 | View Details |
| 27 | (1, 27), (3, 9) | 2 | View Details |
| 75 | (1, 75), (3, 25), (5, 15) | 3 | View Details |
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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 126 is abundant because the sum of its proper divisors (186) exceeds 126.
The smallest abundant number is 12, whose proper divisors are 1, 2, 3, 4, and 6, which sum to 16.