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Factor Pairs of 420
All Factor Pairs of 420
Here are all the factor pairs of 420:
(1, 420)
(2, 210)
(3, 140)
(4, 105)
(5, 84)
(6, 70)
(7, 60)
(10, 42)
(12, 35)
(14, 30)
(15, 28)
(20, 21)
Total: 12 factor pairs
Visual Representation of Factors
These are all the factors of 420:
1
2
3
4
5
6
7
10
12
14
15
20
21
28
30
35
42
60
70
84
105
140
210
420
Properties of 420
Number Type
Abundant Number
Sum of All Factors
1,344
Sum of Proper Divisors
924
Total Factors
24
Prime Factorization
22 × 3 × 5 × 7
Perfect Square?
No
How to Calculate Factor Pairs of 420
Step-by-Step Process
To find all factor pairs of 420, we need to identify all integers that divide 420 evenly (with no remainder).
- Start with the smallest factor, which is always 1
- Check each integer from 1 up to the square root of 420 (v420 ≈ 20.49)
- For each factor found, its corresponding pair is calculated by dividing 420 by that factor
Calculation Example
Let's work through finding the factor pairs of 420:
| Factor Check | Division | Result | Factor Pair |
|---|---|---|---|
| 420 ÷ 1 | 420.00 | Integer result | (1, 420) |
| 420 ÷ 2 | 210.00 | Integer result | (2, 210) |
| 420 ÷ 3 | 140.00 | Integer result | (3, 140) |
| 420 ÷ 4 | 105.00 | Integer result | (4, 105) |
| 420 ÷ 5 | 84.00 | Integer result | (5, 84) |
| 420 ÷ 6 | 70.00 | Integer result | (6, 70) |
| 420 ÷ 7 | 60.00 | Integer result | (7, 60) |
| 420 ÷ 8 | 52.50 | Not a divisor | - |
| 420 ÷ 9 | 46.67 | Not a divisor | - |
| 420 ÷ 10 | 42.00 | Integer result | (10, 42) |
| 420 ÷ 11 | 38.18 | Not a divisor | - |
| 420 ÷ 12 | 35.00 | Integer result | (12, 35) |
| 420 ÷ 13 | 32.31 | Not a divisor | - |
| 420 ÷ 14 | 30.00 | Integer result | (14, 30) |
| 420 ÷ 15 | 28.00 | Integer result | (15, 28) |
| 420 ÷ 16 | 26.25 | Not a divisor | - |
| 420 ÷ 17 | 24.71 | Not a divisor | - |
| 420 ÷ 18 | 23.33 | Not a divisor | - |
| 420 ÷ 19 | 22.11 | Not a divisor | - |
| 420 ÷ 20 | 21.00 | Integer result | (20, 21) |
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 |
| 15 | (1, 15), (3, 5) | 2 | View Details |
| 24 | (1, 24), (2, 12), (3, 8), (4, 6) | 4 | View Details |
| 28 | (1, 28), (2, 14), (4, 7) | 3 | View Details |
| 55 | (1, 55), (5, 11) | 2 | View Details |
| 81 | (1, 81), (3, 27), (9, 9) | 3 | 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 420 is abundant because the sum of its proper divisors (924) exceeds 420.
The smallest abundant number is 12, whose proper divisors are 1, 2, 3, 4, and 6, which sum to 16.