Factor Calculator: Find All Factors and Factor Pairs of a Number
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360 has 24 factors, from 1 to 360. Its prime factorization is 23 × 32 × 5.
360 has 24 factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. Its prime factorization is 2^3 × 3^2 × 5.
Factor pairs
| Factor | Times | Equals |
|---|---|---|
| 1 | 360 | 360 |
| 2 | 180 | 360 |
| 3 | 120 | 360 |
| 4 | 90 | 360 |
| 5 | 72 | 360 |
| 6 | 60 | 360 |
| 8 | 45 | 360 |
| 9 | 40 | 360 |
| 10 | 36 | 360 |
| 12 | 30 | 360 |
| 15 | 24 | 360 |
| 18 | 20 | 360 |
All factors in order
| Factor |
|---|
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |
| 6 |
| 8 |
| 9 |
| 10 |
| 12 |
| 15 |
| 18 |
Show the steps
- Divide by every number up to the square root of 360 (about 18). Each one that divides evenly gives a factor pair.
- Prime factorization: 360 = 2^3 × 3^2 × 5.
- Number of factors = (3 + 1) × (2 + 1) × (1 + 1) = 24.
Counting and adding factors
If n = p1^a × p2^b × …, the number of factors is (a + 1)(b + 1)…
The sum of factors is (1 + p1 + … + p1^a)(1 + p2 + … + p2^b)…
Estimates for planning and learning, not financial, tax, legal or medical advice. Check figures with your lender, tax preparer or doctor before you act.
About this calculator
A factor of a number divides it with no remainder. This calculator lists all of them, groups them into factor pairs, and gives the prime factorization. It also tells you how many factors there are, what they add up to, and whether the number is prime, composite or a perfect square.
Numbers up to one trillion work. The page tests divisors only up to the square root, which is why even large numbers answer instantly.
How to use it
- Type a whole number from 1 to 1,000,000,000,000.
- Read the factor count and prime factorization in the green box.
- Use the factor pair table, or open Show the steps to see how it was found.
How to find factors
Divide the number by 1, 2, 3 and so on up to its square root. Every division with no remainder gives a pair: if 6 divides 360, so does 360 ÷ 6 = 60. You do not need to test past the square root because the second number in each pair is bigger.
Prime or composite?
A prime number has exactly two factors, 1 and itself. A composite number has more than two. The number 1 is neither. Perfect squares such as 36 have an odd number of factors, because the square root pairs with itself.
Perfect, abundant and deficient numbers
Add the factors of a number that are smaller than it. If the sum equals the number, it is perfect (6 and 28). If it is bigger, the number is abundant (12). If it is smaller, the number is deficient (8).
Sources
Quick check: test yourself
How many factors does 48 have?
Correct answer: 10. List the factor pairs of 48 and count each factor once.
Which number has exactly two factors?
Correct answer: A prime number. A prime has only 1 and itself as factors.
Which numbers have an odd number of factors?
Correct answer: Perfect squares. Factors pair up, except the square root of a perfect square, which pairs with itself.
Pick an answer for each question.
Common questions
How do I find all the factors of a number?
Test each whole number from 1 up to the square root. Each one that divides evenly gives two factors, itself and the quotient.
How many factors does 360 have?
24. The prime factorization 2^3 × 3^2 × 5 gives (3 + 1)(2 + 1)(1 + 1) = 24.
What are factor pairs?
Two whole numbers whose product is the number. The factor pairs of 12 are 1 × 12, 2 × 6 and 3 × 4.
Is 1 a prime number?
No. A prime has exactly two factors, and 1 has only one.
What is the difference between a factor and a multiple?
A factor divides the number. A multiple is what you get by multiplying it. 3 is a factor of 12, and 12 is a multiple of 3.
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