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
Number
360
24 Factors
Composite1
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
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
Division Steps
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
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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