Factor Calculator
Find all factors, prime factorization, factor pairs, and test divisibility rules
Calculate Factors
Enter any positive integer up to 1,000,000
Common Factor Examples
Factors of 12:
1, 2, 3, 4, 6, 12
6 factors total
Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
8 factors total
Factors of 17:
1, 17
Prime number - 2 factors
Factor Tips
Every number has at least two factors: 1 and itself
Prime numbers have exactly two factors
Factors come in pairs that multiply to give the original number
Perfect squares have an odd number of factors
Understanding Factors and Factorization
What is a Factor?
A factor is a number that divides evenly into another number with no remainder. Factors are fundamental in mathematics and help us understand the structure of numbers.
Types of Factorization:
- •All Factors: Every number that divides the input evenly
- •Prime Factorization: Breaking down into prime number components
- •Factor Pairs: Numbers that multiply together to give the original
Mathematical Applications
Simplifying Fractions
Find common factors to reduce fractions to lowest terms
Finding GCD and LCM
Use prime factorization to find greatest common divisor and least common multiple
Solving Equations
Factor polynomials and solve quadratic equations
Cryptography
RSA encryption relies on difficulty of factoring large numbers
Key Divisibility Rules
Rule of 2
A number is divisible by 2 if it's even (ends in 0, 2, 4, 6, or 8)
Rule of 3
A number is divisible by 3 if the sum of its digits is divisible by 3
Rule of 5
A number is divisible by 5 if it ends in 0 or 5
Rule of 9
A number is divisible by 9 if the sum of its digits is divisible by 9
Rule of 4
A number is divisible by 4 if its last two digits form a number divisible by 4
Rule of 8
A number is divisible by 8 if its last three digits form a number divisible by 8