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Show all factor pairs, prime factorization,
sum of factors (divisors), aliquot sum,
and prime power decomposition of 72
1) 0 < Factor Pairs ≤ 72
2) The factor pair product = 72
Number | Factor Pairs | Factor Pairs Sum |
---|---|---|
72 | 1 x 72 | 73 |
72 | 2 x 36 | 38 |
72 | 3 x 24 | 27 |
72 | 4 x 18 | 22 |
72 | 6 x 12 | 18 |
72 | 8 x 9 | 17 |
There are 6 factor pairs of 72
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
τ(72) = 12
1, 3, 9
2, 4, 6, 8, 12, 18, 24, 36, 72
Proper factors are all factors except for the number itself
in this case 72
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36
72 = 2 x 36 <--- 2 is a prime number
Reduce 36 to the product of primes:
36 = 3 x 12 <--- 3 is a prime number
Reduce 12 to the product of primes:
12 = 2 x 6 <--- 2 is a prime number
Reduce 6 to the product of primes:
6 = 3 x 2 <--- 3 is a prime number
Reduce 2 to the product of primes:
2 x 2 x 2 x 3 x 3
23 x 32
1 + 72 + 2 + 36 + 3 + 24 + 4 + 18 + 6 + 12 + 8 + 9 = 195
This is the sum of all the factors except the number
1 + 2 + 36 + 3 + 24 + 4 + 18 + 6 + 12 + 8 + 9 = 123