Enter Number
Show all factor pairs, prime factorization,
sum of factors (divisors), aliquot sum,
and prime power decomposition of 72
Factor Pair Logic Rules
1) 0 < Factor Pairs ≤ 72
2) The factor pair product = 72
Factor Pairs Table
| 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
List factors of 72 also known as τ(72)
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
τ(72) = 12
List odd factors of 72
1, 3, 9
List even factors of 72
2, 4, 6, 8, 12, 18, 24, 36, 72
Calculate proper factors of 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
Prime factorization for 72
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:
Show prime factorization:
2 x 2 x 2 x 3 x 3
Prime Power Decomposition
23 x 32
Show the sum of factors (divisors) for 72
1 + 72 + 2 + 36 + 3 + 24 + 4 + 18 + 6 + 12 + 8 + 9 = 195
Show the aliquot sum:
This is the sum of all the factors except the number
1 + 2 + 36 + 3 + 24 + 4 + 18 + 6 + 12 + 8 + 9 = 123
Common Core State Standards In This Lesson
What is the Answer?
How does the Factorization Calculator work?
1) Factor pairs and prime factorization and prime power decomposition
2) Factors and Proper Factors 3) Aliquot Sum
This calculator has 1 input.
What 3 formulas are used for the Factorization Calculator?
For factors in step 1, find the prime factorization for each number
What 7 concepts are covered in the Factorization Calculator?
- aliquot sum
- aliquot sum is the sum of all the factors of a number except the number itself
- digit
- Any of the numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) used to construct a number
- factor
- a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.
- factorization
- power
- how many times to use the number in a multiplication
- prime number
- a natural number greater than 1 that is not a product of two smaller natural numbers.
- sum
- the total amount resulting from the addition of two or more numbers, amounts, or items
