Show Factorization for 40

Enter Number

Show all factor pairs, prime factorization,

sum of factors (divisors), aliquot sum,

and prime power decomposition of 40

Factor Pair Logic Rules

1) 0 < Factor Pairs ≤ 40

2) The factor pair product = 40

Factor Pairs Table

Number	Factor Pairs	Factor Pairs Sum
40	1 x 40	41
40	2 x 20	22
40	4 x 10	14
40	5 x 8	13

There are 4 factor pairs of 40

List factors of 40 also known as τ(40)

1, 2, 4, 5, 8, 10, 20, 40

τ(40) = 8

List odd factors of 40

1, 5

List even factors of 40

2, 4, 8, 10, 20, 40

Calculate proper factors of 40

Proper factors are all factors except for the number itself
in this case 40

1, 2, 4, 5, 8, 10, 20

Prime factorization for 40

40 = 2 x 20 <--- 2 is a prime number

Reduce 20 to the product of primes:

20 = 5 x 4 <--- 5 is a prime number

Reduce 4 to the product of primes:

4 = 2 x 2 <--- 2 is a prime number

Reduce 2 to the product of primes:

Show prime factorization:

2 x 2 x 2 x 5

Prime Power Decomposition

2³ x 5

Show the sum of factors (divisors) for 40

1 + 40 + 2 + 20 + 4 + 10 + 5 + 8 = 90

Show the aliquot sum:

This is the sum of all the factors except the number

1 + 2 + 20 + 4 + 10 + 5 + 8 = 50

Common Core State Standards In This Lesson

4.OA.A.4

What is the Answer?

1, 2, 4, 5, 8, 10, 20, 40

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.

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

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