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Factor Pairs of 84
All Factor Pairs of 84
Here are all the factor pairs of 84:
(1, 84)
(2, 42)
(3, 28)
(4, 21)
(6, 14)
(7, 12)
Total: 6 factor pairs
Visual Representation of Factors
These are all the factors of 84:
1
2
3
4
6
7
12
14
21
28
42
84
Properties of 84
Number Type
Abundant Number
Sum of All Factors
224
Sum of Proper Divisors
140
Total Factors
12
Prime Factorization
22 × 3 × 7
Perfect Square?
No
How to Calculate Factor Pairs of 84
Step-by-Step Process
To find all factor pairs of 84, we need to identify all integers that divide 84 evenly (with no remainder).
- Start with the smallest factor, which is always 1
- Check each integer from 1 up to the square root of 84 (v84 ≈ 9.17)
- For each factor found, its corresponding pair is calculated by dividing 84 by that factor
Calculation Example
Let's work through finding the factor pairs of 84:
| Factor Check | Division | Result | Factor Pair |
|---|---|---|---|
| 84 ÷ 1 | 84.00 | Integer result | (1, 84) |
| 84 ÷ 2 | 42.00 | Integer result | (2, 42) |
| 84 ÷ 3 | 28.00 | Integer result | (3, 28) |
| 84 ÷ 4 | 21.00 | Integer result | (4, 21) |
| 84 ÷ 5 | 16.80 | Not a divisor | - |
| 84 ÷ 6 | 14.00 | Integer result | (6, 14) |
| 84 ÷ 7 | 12.00 | Integer result | (7, 12) |
| 84 ÷ 8 | 10.50 | Not a divisor | - |
| 84 ÷ 9 | 9.33 | Not a divisor | - |
Explore More Factor Pairs
Check out factor pairs of these randomly selected numbers:
| Number | Factor Pairs | Total Pairs | Details |
|---|---|---|---|
| 18 | (1, 18), (2, 9), (3, 6) | 3 | View Details |
| 19 | (1, 19) | 1 | View Details |
| 36 | (1, 36), (2, 18), (3, 12), (4, 9), (6, 6) | 5 | View Details |
| 64 | (1, 64), (2, 32), (4, 16), (8, 8) | 4 | View Details |
| 65 | (1, 65), (5, 13) | 2 | 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 84 is abundant because the sum of its proper divisors (140) exceeds 84.
The smallest abundant number is 12, whose proper divisors are 1, 2, 3, 4, and 6, which sum to 16.