Factor Calculator - Find All Factors & Prime Factorization

Find All Factors

Enter a number:

Number: 60 COMPOSITE
Total Factors: 12
Sum of Factors: 168
Product of Factors: 60⁶ = 46,656,000,000

All Factors of 60:

1

2

3

4

5

6

10

12

15

20

30

60

Divisibility Tests:

÷2 ✓ ÷3 ✓ ÷4 ✓ ÷5 ✓ ÷6 ✓ ÷7 ✗ ÷8 ✗ ÷9 ✗ ÷10 ✓

12

24

36

48

72

100

120

144

Prime Factorization

Enter a number:

Prime Factorization of 60:
Standard Form: 60 = 2² × 3¹ × 5¹
Expanded Form: 60 = 2 × 2 × 3 × 5
Exponential Form: 60 = 2² × 3 × 5
Prime Factors: 2, 3, 5
Exponents: 2, 1, 1

Step-by-Step Division:

60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Prime factors: 2, 2, 3, 5

Factor Pairs

Enter a number:

Factor Pairs of 60:

1 × 60

2 × 30

3 × 20

4 × 15

5 × 12

6 × 10

Total Factor Pairs: 6
Perfect Square: No (no factor pairs itself)
Closest to Square Root: 6 × 10 (√60 ≈ 7.75)

Factor Tree

Enter a number:

                    60
                   ╱  ╲
                  4    15
                 ╱╲   ╱ ╲
                2  2  3   5
                
Prime Factorization: 2² × 3 × 5 = 60

Factor Tree Explanation:
1. Start with 60
2. Divide by 4 and 15 (60 = 4 × 15)
3. Factor 4 = 2 × 2
4. Factor 15 = 3 × 5
5. All factors are now prime: 2, 2, 3, 5
Result: 60 = 2² × 3 × 5

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Factor Calculator — quick guide

1) Core idea

Find all factors of n, its prime factorization, factor pairs, and a simple factor tree. Factors are integers that divide n with no remainder.

2) How this tool works

All Factors: tests divisors up to √n and mirrors pairs.
Prime Factorization: repeated division; shows standard and expanded forms.
Factor Pairs: lists (a, b) with a × b = n and a ≤ b.
Factor Tree: builds a simple split until primes.

3) Sanity checks

n = 1 → no prime factorization; factors = {1}.
n = 13 → prime (factors: 1, 13 only).
n = 36 → pairs include 6×6 (perfect square).

4) Shortcuts that help

Stop trial division at √n; add both d and n/d.
If n = p1^a1 · p2^a2 · … then count of factors = Π(ai+1).
Use divisibility rules (2,3,5,9,10) for quick pruning.

5) Common pitfalls

Confusing factors with multiples.
Forgetting the √n duplicate when n is a perfect square.
Very large n: this tool caps inputs to keep it responsive.

6) Micro-examples

60 → factors: 1,2,3,4,5,6,10,12,15,20,30,60.
60 → prime factorization: 2^2 × 3 × 5.
60 → factor pairs: (1,60), (2,30), (3,20), (4,15), (5,12), (6,10).

7) Mini-FAQ

Negative numbers? This tool expects positive integers.
Zero? Not supported; every integer divides 0.
Prime check? Reported via PRIME/COMPOSITE badge.

8) Action tip

When n is large, compute prime factorization first—then derive counts, sums, and pairs systematically.