Factor Calculator

Direct answer

A factor of a number is a whole number that divides it with no remainder. For example, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 — 12 factors in total. Prime factorization breaks a number into prime factors: 60 = 2² × 3 × 5. Enter any whole number below and the tool lists all its factors, its factor pairs, its prime factorization, and whether it is prime or composite.

Inputs

Field	Default	Unit
Whole number	60	—

Outputs

Output	How it is found	Default result (60)
All factors	Test every divisor up to the square root of the number	1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Total factor count	Count of the factors	12
Factor pairs	Each divisor paired with its quotient	1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10
Prime factorization	Repeated division by prime numbers	60 = 2² × 3 × 5
Prime or composite	More than two factors means composite; exactly two means prime	60 is a composite number

Defaults on load: 60 → 12 factors, prime factorization 2² × 3 × 5, composite. The result shows as soon as the page loads, before you enter anything.

How it works

1. Find the factors by testing divisors up to the square root. To factor 60, test 1, 2, 3, 4, 5, 6 and 7 (√60 ≈ 7.75, so testing up to 7 is enough). Every divisor found gives two factors at once: the divisor and its quotient. For example, 60 ÷ 5 = 12, so both 5 and 12 are factors. Testing past the square root only repeats pairs already found.
2. Pair them up. Each divisor and its quotient form a factor pair: 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10. Every pair multiplies back to the original number.
3. Prime factorization by repeated division. Divide by the smallest prime that goes in evenly, and repeat on the quotient until only 1 is left: 60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5, 5 ÷ 5 = 1. Collect the divisors: 2 × 2 × 3 × 5, written with exponents as 2² × 3 × 5.
4. Prime or composite. A number with exactly two factors (1 and itself) is prime. A number with more than two factors is composite. The number 1 has only one factor, so it is neither prime nor composite.

Factors of 1–20

Number	Factors	Count
1	1	1
2	1, 2	2
3	1, 3	2
4	1, 2, 4	3
5	1, 5	2
6	1, 2, 3, 6	4
7	1, 7	2
8	1, 2, 4, 8	4
9	1, 3, 9	3
10	1, 2, 5, 10	4
11	1, 11	2
12	1, 2, 3, 4, 6, 12	6
13	1, 13	2
14	1, 2, 7, 14	4
15	1, 3, 5, 15	4
16	1, 2, 4, 8, 16	5
17	1, 17	2
18	1, 2, 3, 6, 9, 18	6
19	1, 19	2
20	1, 2, 4, 5, 10, 20	6

Prime numbers in this range (exactly two factors) are 2, 3, 5, 7, 11, 13, 17 and 19. Perfect squares — 1, 4, 9, 16 — have an odd number of factors, because their square root pairs with itself (for example, 4 × 4 = 16). Once you have the factors, the LCM calculator finds the smallest number two numbers share as a multiple, and the math calculator covers the basic add, subtract, multiply and divide steps behind all of it.

Worked examples

Example 1 — The default: factors of 60

Test divisors up to √60 ≈ 7.75, so 1 through 7.

• Divisors that divide 60 evenly: 1, 2, 3, 4, 5, 6 (7 does not: 60 ÷ 7 = 8.57…)
• Full factor list: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 — 12 factors
• Factor pairs: 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10 — 6 pairs
• Prime factorization: 60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5, 5 ÷ 5 = 1 → 60 = 2² × 3 × 5
• 12 factors is more than two, so 60 is composite.

Example 2 — A perfect square: factors of 36

Test divisors up to √36 = 6.

• Full factor list: 1, 2, 3, 4, 6, 9, 12, 18, 36 — 9 factors
• Factor pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6 — 5 pairs (6 × 6 is the middle pair, which is why the count is odd)
• Prime factorization: 36 ÷ 2 = 18, 18 ÷ 2 = 9, 9 ÷ 3 = 3, 3 ÷ 3 = 1 → 36 = 2² × 3²
• 36 is composite.

Example 3 — A prime number: factors of 97

Test divisors up to √97 ≈ 9.85, so 2 through 9. None of 2, 3, 4, 5, 6, 7, 8 or 9 divides 97 evenly.

• Full factor list: 1, 97 — 2 factors
• Factor pairs: 1 × 97 — 1 pair
• Prime factorization: 97 = 97 (97 is itself prime)
• Exactly two factors, so 97 is prime.

Example 4 — A round number: factors of 100

Test divisors up to √100 = 10.

• Full factor list: 1, 2, 4, 5, 10, 20, 25, 50, 100 — 9 factors
• Factor pairs: 1 × 100, 2 × 50, 4 × 25, 5 × 20, 10 × 10 — 5 pairs
• Prime factorization: 100 ÷ 2 = 50, 50 ÷ 2 = 25, 25 ÷ 5 = 5, 5 ÷ 5 = 1 → 100 = 2² × 5²
• 100 is composite.

Tips and mistakes

• Stop at the square root. Once you pass √n, every divisor you find is a repeat of a pair already found. For 60, √60 ≈ 7.75, so testing 1–7 finds all 12 factors.
• Do not forget 1 and the number itself. Every positive whole number has 1 and itself as factors. A common mistake is listing only the “middle” factors and missing these two.
• Do not confuse factors with multiples. Factors divide a number (factors of 12 are 1, 2, 3, 4, 6, 12); multiples are what you get by multiplying it (multiples of 12 are 12, 24, 36, 48, …). Factors are finite; multiples go on forever.
• 1 is neither prime nor composite. It has only one factor (itself), so it fails both definitions. Saying “1 is prime” is the most common factor mistake.
• Prime factorization is unique. Every whole number greater than 1 breaks into exactly one set of prime factors (in a different order at most). That is why 60 is always 2² × 3 × 5 and never anything else.
• Use prime factorization for GCD and LCM. The greatest common divisor of 48 and 60 is 12 (48 = 2⁴ × 3, 60 = 2² × 3 × 5, shared primes 2² × 3 = 12). The least common multiple of 12 and 18 is 36 (12 = 2² × 3, 18 = 2 × 3², highest powers 2² × 3² = 36).

Sources

Factorisation is standard number theory — see Prime Factorization on MathWorld. Reviewed by the Average Calculator Team. Last reviewed: 7 November 2026.

Frequently asked questions

What is a factor of a number?

A factor is a whole number that divides another number with no remainder. For example, 5 is a factor of 60 because 60 ÷ 5 = 12 exactly. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

How do you find all the factors of a number?

Test every whole number from 1 up to the square root of the number. Each divisor that divides evenly gives two factors: itself and its quotient. For 60, the square root is about 7.75, so testing 1 to 7 finds divisors 1, 2, 3, 4, 5 and 6, which give all 12 factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

What is prime factorization?

Prime factorization breaks a number into prime factors by repeated division. Divide by the smallest prime that goes in evenly and repeat until only 1 is left. For 60: 60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5, 5 ÷ 5 = 1, so 60 = 2² × 3 × 5.

How do you know if a number is prime?

A prime number has exactly two factors: 1 and itself. Test divisors up to its square root — if none divides evenly, it is prime. For example, 97 has only the factors 1 and 97, so 97 is prime. The number 1 is neither prime nor composite because it has only one factor.

What is the difference between factors and multiples?

Factors divide a number: the factors of 12 are 1, 2, 3, 4, 6 and 12. Multiples are made by multiplying a number: the multiples of 12 are 12, 24, 36, 48 and so on. A number has a finite set of factors but infinitely many multiples.

What are factor pairs?

A factor pair is two factors that multiply to the original number. The factor pairs of 60 are 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12 and 6 × 10. Every factor belongs to exactly one pair, and a perfect square such as 36 has one pair where both numbers are the same: 6 × 6.

Disclaimer

This calculator works with positive whole numbers up to 100,000,000 and shows exact arithmetic results for the number entered. It is a general-purpose math tool for learning and checking homework, not a substitute for a teacher or textbook. Results are only as correct as the number entered.

Related calculators

• Average Calculator Online — the homepage average tool
• Fraction Calculator — fraction arithmetic, where factors simplify fractions
• Scientific Calculator — powers, roots and scientific functions
• Percentage Calculator — percentage calculations
• Ratio Calculator — ratios, simplified using the greatest common divisor

Last updated: November 7, 2026.