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📘 About the Factor Calculator
The factors of a number are the whole numbers that divide it exactly: 12 has factors 1, 2, 3, 4, 6 and 12. Prime factorisation writes it as a product of primes (12 = 2² × 3) — the ‘DNA’ of the number, used for HCF and LCM, simplifying fractions and roots, and cryptography.
Enter a whole number up to a trillion. The calculator lists all factors and factor pairs, the prime factorisation, how many factors there are (from the exponents), their sum, and whether the number is prime, perfect, abundant, deficient or a perfect square.
🧮 Formula
✏️ Worked examples
Factors of 360
You get| Factors of 360 | 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 |
| Prime factorisation | 2³ × 3² × 5 |
| Number of factors | 24 (from exponents: (3 + 1) × (2 + 1) × (1 + 1)) |
| Sum of factors | 1,170 |
| Type | Composite number |
| Perfect / abundant / deficient | Abundant (proper factors add up to more: 810) |
| Perfect square? | No (√360 ≈ 18.973666) |
| Prime factors | 2, 3, 5 |
2³ × 3² × 5.
A perfect number
You get| Factors of 28 | 1, 2, 4, 7, 14, 28 |
| Prime factorisation | 2² × 7 |
| Number of factors | 6 (from exponents: (2 + 1) × (1 + 1)) |
| Sum of factors | 56 |
| Type | Composite number |
| Perfect / abundant / deficient | Perfect number (its proper factors add up to it) |
| Perfect square? | No (√28 ≈ 5.2915026) |
| Prime factors | 2, 7 |
1, 2, 4, 7, 14, 28.
🧭 How to use this calculator
What you get
- Factors of 360
- Prime factorisation
- Number of factors
- Sum of factors
- Type
- Perfect / abundant / deficient
- Perfect square?
- Prime factors
❓ Frequently asked questions
How do you find all factors of a number?
Test divisors from 1 up to √n; each divisor d gives the pair d and n/d.
What is prime factorisation?
Writing a number as a product of prime numbers. Every whole number above 1 has exactly one (the fundamental theorem of arithmetic).
How many factors does 360 have?
24, because 360 = 2³ × 3² × 5 and (3 + 1)(2 + 1)(1 + 1) = 24.
