◆ MATH · NUMBER THEORY

Factor Calculator

Find all factors, prime factorization, and factor pairs of any number. Includes divisibility rules check, number properties, and factor count chart for nearby numbers.

24

Factor Count

1,170

Sum of Factors

Abundant

Number Type

Enter a Number

Quick Examples

Number

360

24 Factors

Composite

1

Smallest Factor

180

Largest Proper Factor

24

Factor Count

1,170

Sum of Factors

810

Sum (Proper)

No

Is Perfect Sq?

All Factors — Click to Explore It

Prime factorComposite factor

Factor Pairs (A × B = N)

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

Prime Factorization

360 = 23 × 32 × 5

Division Steps

÷2360 ÷ 2 = 1802 is prime
÷2180 ÷ 2 = 902 is prime
÷290 ÷ 2 = 452 is prime
÷345 ÷ 3 = 153 is prime
÷315 ÷ 3 = 53 is prime
÷55 ÷ 5 = 15 is prime

Number Properties

🔢

Type

Composite

🔴

Is Prime

No

🟦

Is Composite

Yes

Perfect Square

No

💎

Perfect Number

No

📈

Abundant

Yes (excess 450)

📉

Deficient

No

🔟

# of Factors

24

Σ

Sum of Factors

1,170

Σ

Sum of Proper Factors

810

Divisibility Rules Check

2

Last digit is 0 → even, so divisible

3

Digit sum is 9 → divisible by 3

4

Last two digits are 60 → divisible by 4

5

Last digit is 0 → 0 or 5, so divisible

6

Divisible by 2: yes, by 3: yes → divisible by 6

7

No simple digit rule — 360 ÷ 7 leaves a remainder

8

Last three digits are 360 → divisible by 8

9

Digit sum is 9 → divisible by 9

10

Last digit is 0 → 0, so divisible

11

Alternating digit sum is -3 → not divisible by 11

Factor Count: N−10 to N+10

35012351835212353235483554356635783584359236024361336243636364123654366836723681036963708

Understanding Factors and Prime Factorization

A factor of a whole number n is any positive integer that divides n exactly, leaving no remainder. Every number greater than 1 has at least two factors — 1 and itself — and numbers with exactly those two are called prime; anything with more is composite. Prime factorization breaks a composite number down into the unique set of prime numbers that multiply together to produce it. The Fundamental Theorem of Arithmetic guarantees this breakdown is one-of-a-kind: aside from the order you write them in, there is only ever one way to express a given integer as a product of primes.

How to Count Factors

If n = p1^a1 × p2^a2 × ... × pk^ak (prime factorization), then:Number of factors = (a1+1)(a2+1)...(ak+1)Example: 360 = 2³ × 3² × 5¹ → (3+1)(2+1)(1+1) = 4×3×2 = 24 factorsSum of factors formula: σ(n) = [(p1^(a1+1)-1)/(p1-1)] × [(p2^(a2+1)-1)/(p2-1)] × ...

Special Number Types

Perfect numbers equal the sum of their own proper factors (excluding themselves) — 6 and 28 are the smallest two. Abundant numbers have proper factors that add up to more than the number itself, like 12 (1+2+3+4+6 = 16). Deficient numbers are the opposite — their proper factors sum to less than the number, which describes most integers, including every prime. Highly composite numbers hold the record for the most factors among all smaller numbers, which is why round, useful numbers like 12, 24, and 60 recur so often in everyday measurement.

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Frequently Asked Questions