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Show all factor pairs, prime factorization,
sum of factors (divisors), aliquot sum,
and prime power decomposition of 100
1) 0 < Factor Pairs ≤ 100
2) The factor pair product = 100
Number | Factor Pairs | Factor Pairs Sum |
---|---|---|
100 | 1 x 100 | 101 |
100 | 2 x 50 | 52 |
100 | 4 x 25 | 29 |
100 | 5 x 20 | 25 |
100 | 10 x 10 | 20 |
There are 5 factor pairs of 100
1, 2, 4, 5, 10, 20, 25, 50, 100
τ(100) = 9
1, 5, 25
2, 4, 10, 20, 50, 100
Proper factors are all factors except for the number itself
in this case 100
1, 2, 4, 5, 10, 20, 25, 50
100 = 2 x 50 <--- 2 is a prime number
Reduce 50 to the product of primes:
50 = 5 x 10 <--- 5 is a prime number
Reduce 10 to the product of primes:
10 = 2 x 5 <--- 2 is a prime number
Reduce 5 to the product of primes:
2 x 2 x 5 x 5
22 x 52
1 + 100 + 2 + 50 + 4 + 25 + 5 + 20 + 10 = 217
This is the sum of all the factors except the number
1 + 2 + 50 + 4 + 25 + 5 + 20 + 10 = 117