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Factor Pairs of 900 Perfect Square
All Factor Pairs of 900
Here are all the factor pairs of 900:
(1, 900)
(2, 450)
(3, 300)
(4, 225)
(5, 180)
(6, 150)
(9, 100)
(10, 90)
(12, 75)
(15, 60)
(18, 50)
(20, 45)
(25, 36)
(30, 30)
Total: 14 factor pairs
Visual Representation of Factors
These are all the factors of 900:
1
2
3
4
5
6
9
10
12
15
18
20
25
30
36
45
50
60
75
90
100
150
180
225
300
450
900
Properties of 900
Number Type
Abundant Number
Sum of All Factors
2,821
Sum of Proper Divisors
1,921
Total Factors
27
Prime Factorization
22 × 32 × 52
Perfect Square?
Yes
How to Calculate Factor Pairs of 900
Step-by-Step Process
To find all factor pairs of 900, we need to identify all integers that divide 900 evenly (with no remainder).
- Start with the smallest factor, which is always 1
- Check each integer from 1 up to the square root of 900 (v900 ≈ 30.00)
- For each factor found, its corresponding pair is calculated by dividing 900 by that factor
Calculation Example
Let's work through finding the factor pairs of 900:
| Factor Check | Division | Result | Factor Pair |
|---|---|---|---|
| 900 ÷ 1 | 900.00 | Integer result | (1, 900) |
| 900 ÷ 2 | 450.00 | Integer result | (2, 450) |
| 900 ÷ 3 | 300.00 | Integer result | (3, 300) |
| 900 ÷ 4 | 225.00 | Integer result | (4, 225) |
| 900 ÷ 5 | 180.00 | Integer result | (5, 180) |
| 900 ÷ 6 | 150.00 | Integer result | (6, 150) |
| 900 ÷ 7 | 128.57 | Not a divisor | - |
| 900 ÷ 8 | 112.50 | Not a divisor | - |
| 900 ÷ 9 | 100.00 | Integer result | (9, 100) |
| 900 ÷ 10 | 90.00 | Integer result | (10, 90) |
| 900 ÷ 11 | 81.82 | Not a divisor | - |
| 900 ÷ 12 | 75.00 | Integer result | (12, 75) |
| 900 ÷ 13 | 69.23 | Not a divisor | - |
| 900 ÷ 14 | 64.29 | Not a divisor | - |
| 900 ÷ 15 | 60.00 | Integer result | (15, 60) |
| 900 ÷ 16 | 56.25 | Not a divisor | - |
| 900 ÷ 17 | 52.94 | Not a divisor | - |
| 900 ÷ 18 | 50.00 | Integer result | (18, 50) |
| 900 ÷ 19 | 47.37 | Not a divisor | - |
| 900 ÷ 20 | 45.00 | Integer result | (20, 45) |
| 900 ÷ 21 | 42.86 | Not a divisor | - |
| 900 ÷ 22 | 40.91 | Not a divisor | - |
| 900 ÷ 23 | 39.13 | Not a divisor | - |
| 900 ÷ 24 | 37.50 | Not a divisor | - |
| 900 ÷ 25 | 36.00 | Integer result | (25, 36) |
| 900 ÷ 26 | 34.62 | Not a divisor | - |
| 900 ÷ 27 | 33.33 | Not a divisor | - |
| 900 ÷ 28 | 32.14 | Not a divisor | - |
| 900 ÷ 29 | 31.03 | Not a divisor | - |
| 900 ÷ 30 | 30.00 | Integer result | (30, 30) |
Explore More Factor Pairs
Check out factor pairs of these randomly selected numbers:
| Number | Factor Pairs | Total Pairs | Details |
|---|---|---|---|
| 3 | (1, 3) | 1 | View Details |
| 12 | (1, 12), (2, 6), (3, 4) | 3 | View Details |
| 24 | (1, 24), (2, 12), (3, 8), (4, 6) | 4 | View Details |
| 72 | (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9) | 6 | View Details |
| 77 | (1, 77), (7, 11) | 2 | View Details |
| 80 | (1, 80), (2, 40), (4, 20), (5, 16), (8, 10) | 5 | 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 900 is abundant because the sum of its proper divisors (1,921) exceeds 900.
The smallest abundant number is 12, whose proper divisors are 1, 2, 3, 4, and 6, which sum to 16.