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Factor Pairs of 840
All Factor Pairs of 840
Here are all the factor pairs of 840:
(1, 840)
(2, 420)
(3, 280)
(4, 210)
(5, 168)
(6, 140)
(7, 120)
(8, 105)
(10, 84)
(12, 70)
(14, 60)
(15, 56)
(20, 42)
(21, 40)
(24, 35)
(28, 30)
Total: 16 factor pairs
Visual Representation of Factors
These are all the factors of 840:
1
2
3
4
5
6
7
8
10
12
14
15
20
21
24
28
30
35
40
42
56
60
70
84
105
120
140
168
210
280
420
840
Properties of 840
Number Type
Abundant Number
Sum of All Factors
2,880
Sum of Proper Divisors
2,040
Total Factors
32
Prime Factorization
23 × 3 × 5 × 7
Perfect Square?
No
How to Calculate Factor Pairs of 840
Step-by-Step Process
To find all factor pairs of 840, we need to identify all integers that divide 840 evenly (with no remainder).
- Start with the smallest factor, which is always 1
- Check each integer from 1 up to the square root of 840 (v840 ≈ 28.98)
- For each factor found, its corresponding pair is calculated by dividing 840 by that factor
Calculation Example
Let's work through finding the factor pairs of 840:
| Factor Check | Division | Result | Factor Pair |
|---|---|---|---|
| 840 ÷ 1 | 840.00 | Integer result | (1, 840) |
| 840 ÷ 2 | 420.00 | Integer result | (2, 420) |
| 840 ÷ 3 | 280.00 | Integer result | (3, 280) |
| 840 ÷ 4 | 210.00 | Integer result | (4, 210) |
| 840 ÷ 5 | 168.00 | Integer result | (5, 168) |
| 840 ÷ 6 | 140.00 | Integer result | (6, 140) |
| 840 ÷ 7 | 120.00 | Integer result | (7, 120) |
| 840 ÷ 8 | 105.00 | Integer result | (8, 105) |
| 840 ÷ 9 | 93.33 | Not a divisor | - |
| 840 ÷ 10 | 84.00 | Integer result | (10, 84) |
| 840 ÷ 11 | 76.36 | Not a divisor | - |
| 840 ÷ 12 | 70.00 | Integer result | (12, 70) |
| 840 ÷ 13 | 64.62 | Not a divisor | - |
| 840 ÷ 14 | 60.00 | Integer result | (14, 60) |
| 840 ÷ 15 | 56.00 | Integer result | (15, 56) |
| 840 ÷ 16 | 52.50 | Not a divisor | - |
| 840 ÷ 17 | 49.41 | Not a divisor | - |
| 840 ÷ 18 | 46.67 | Not a divisor | - |
| 840 ÷ 19 | 44.21 | Not a divisor | - |
| 840 ÷ 20 | 42.00 | Integer result | (20, 42) |
| 840 ÷ 21 | 40.00 | Integer result | (21, 40) |
| 840 ÷ 22 | 38.18 | Not a divisor | - |
| 840 ÷ 23 | 36.52 | Not a divisor | - |
| 840 ÷ 24 | 35.00 | Integer result | (24, 35) |
| 840 ÷ 25 | 33.60 | Not a divisor | - |
| 840 ÷ 26 | 32.31 | Not a divisor | - |
| 840 ÷ 27 | 31.11 | Not a divisor | - |
| 840 ÷ 28 | 30.00 | Integer result | (28, 30) |
Explore More Factor Pairs
Check out factor pairs of these randomly selected numbers:
| Number | Factor Pairs | Total Pairs | Details |
|---|---|---|---|
| 10 | (1, 10), (2, 5) | 2 | View Details |
| 12 | (1, 12), (2, 6), (3, 4) | 3 | View Details |
| 26 | (1, 26), (2, 13) | 2 | View Details |
| 67 | (1, 67) | 1 | View Details |
| 120 | (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), (10, 12) | 8 | View Details |
| 144 | (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), (12, 12) | 8 | 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 840 is abundant because the sum of its proper divisors (2,040) exceeds 840.
The smallest abundant number is 12, whose proper divisors are 1, 2, 3, 4, and 6, which sum to 16.