Show all factor pairs, prime factorization,
sum of factors (divisors), aliquot sum,
and prime power decomposition of 100
Factor Pair Logic Rules
1) 0 < Factor Pairs ≤ 100
2) The factor pair product = 100
Factor Pairs Table
| 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
List factors of 100 also known as τ(100)
1, 2, 4, 5, 10, 20, 25, 50, 100
τ(100) = 9
List odd factors of 100
1, 5, 25
List even factors of 100
2, 4, 10, 20, 50, 100
Calculate proper factors of 100
Proper factors are all factors except for the number itself
in this case 100
1, 2, 4, 5, 10, 20, 25, 50
Prime factorization for 100
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:
Show prime factorization:
2 x 2 x 5 x 5
Prime Power Decomposition
22 x 52
Show the sum of factors (divisors) for 100
1 + 100 + 2 + 50 + 4 + 25 + 5 + 20 + 10 = 217
Show the aliquot sum:
This is the sum of all the factors except the number
1 + 2 + 50 + 4 + 25 + 5 + 20 + 10 = 117
Common Core State Standards In This Lesson
4.OA.A.4
What is the Answer?
1, 2, 4, 5, 10, 20, 25, 50, 100
How does the Factorization Calculator work?
Free Factorization Calculator - Given a positive integer, this calculates the following for that number:
1) Factor pairs and prime factorization and prime power decomposition
2) Factors and Proper Factors 3) Aliquot Sum
This calculator has 1 input.
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?
Find all pairs that have a product equal to the number you want to factor
For factors in step 1, find the prime factorization for each number
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
