Use this factor calculator to list all factors of a positive integer. It helps with divisibility checks, number properties, and building intuition for greatest common factors and least common multiples.
Factors are numbers that divide evenly into another number with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 without leaving a remainder. Finding all factors of a number is called factorization.
To find all factors of a number, you can follow these steps: 1) Start with 1 and the number itself (these are always factors). 2) Check all integers from 2 up to the square root of the number. 3) If a number divides evenly (with no remainder), it's a factor. 4) For each factor you find, its pair (the number divided by the factor) is also a factor. This calculator automates this process for you.
Tip: prime numbers only have two factors, 1 and the number itself.
Let's look at some examples: - Factors of 12: 1, 2, 3, 4, 6, 12 - Factors of 20: 1, 2, 4, 5, 10, 20 - Factors of 7: 1, 7 (Prime numbers only have two factors: 1 and themselves) - Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
12 can be divided evenly by several smaller integers.
12 ÷ 1, 2, 3, 4, 6, 12
Result: 1, 2, 3, 4, 6, 12
20 has six positive factors because several integers divide into it with no remainder.
20 ÷ 1, 2, 4, 5, 10, 20
Result: 1, 2, 4, 5, 10, 20
A prime number has only two positive factors.
7 ÷ 1, 7
Result: 1, 7
36 has many factors because it is highly composite and can be split in multiple ways.
36 ÷ 1, 2, 3, 4, 6, 9, 12, 18, 36
Result: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factorization has many practical applications in mathematics and everyday life: - Simplifying fractions - Finding the Greatest Common Factor (GCF) - Solving algebraic equations - Cryptography and computer security - Number theory research - Computer algorithms and optimization
A factor calculator lists all positive integers that divide evenly into the number you enter.
Factors divide a number evenly, while multiples are numbers produced by multiplying the original number by whole numbers.
Every positive integer is divisible by 1 and by itself with no remainder, so those two values are always part of the factor list.
Factors make it easier to simplify fractions and find the greatest common factor shared by two or more numbers.
