Factor Calculator Online Free Tool
Factor Calculator
Factor Calculator
Please provide an integer to calculate its factors and prime factors.
Instructions: Enter any positive integer to see all its factors, prime factorization, factor pairs, and number classification. The calculator will automatically analyze the number and display detailed results including whether it's prime, perfect, deficient, or abundant.
The factor calculator finds all factors (divisors) of any positive integer. A factor of a number divides it evenly with no remainder. Enter any number to instantly see all its factors, factor pairs, and whether the number is prime, composite, or a perfect square.
Finding Factors
A factor of n is any positive integer that divides n evenly. To find all factors, test every integer from 1 to √n -- if a number divides evenly, both the divisor and the quotient are factors.
Factors of 36: Test 1: 36/1=36 ✓ → factors: 1, 36 Test 2: 36/2=18 ✓ → factors: 2, 18 Test 3: 36/3=12 ✓ → factors: 3, 12 Test 4: 36/4=9 ✓ → factors: 4, 9 Test 5: 36/5=7.2 ✗ Test 6: 36/6=6 ✓ → factor: 6 (pair with itself) All factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Only need to test up to √n. For 36, √36=6, so stop at 6.
Factor Pairs
Factor pairs are two factors whose product equals the original number. 36 has factor pairs: (1,36), (2,18), (3,12), (4,9), (6,6). The number of factors a number has depends on its prime factorization: if n = p₁^a × p₂^b..., then the total number of factors = (a+1)(b+1)...
Frequently Asked Questions
What is the difference between factors and multiples?⌄
Factors of n are numbers that divide n evenly (smaller than or equal to n). Multiples of n are numbers that n divides evenly (larger than or equal to n). Factors of 6: 1, 2, 3, 6. Multiples of 6: 6, 12, 18, 24... Factors go down (or equal); multiples go up.
What is a prime number?⌄
A prime number has exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13... A composite number has more than two factors (is divisible by something other than 1 and itself). 1 is neither prime nor composite by convention.
What is a perfect number?⌄
A perfect number equals the sum of all its proper factors (factors excluding the number itself). 6 = 1+2+3. 28 = 1+2+4+7+14. The next perfect numbers are 496 and 8128. Perfect numbers are extremely rare -- only 51 are known, all even.
How do factors relate to fractions?⌄
Factors are essential for simplifying fractions. To simplify a fraction, divide both numerator and denominator by their greatest common factor (GCF). To simplify 18/24: GCF(18,24) = 6. 18/6 = 3, 24/6 = 4. Simplified: 3/4.