The factors of 72 are all the numbers that divide 72 exactly (without leaving a remainder). The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. That gives 72 a total of 12 factors. The prime factorization of 72 is 2³ × 3².
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 (total 12 factors).
Prime factorization: 72 = 2³ × 3².
Factor pairs: (1,72), (2,36), (3,24), (4,18), (6,12), (8,9).
Number of factors = (3+1)(2+1) = 12.
72 is NOT a perfect square (exponent of 2 is odd).
√72 = 6√2 ≈ 8.49.
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Total number of factors: 12
Verification (check each divides 72 exactly): 72 ÷ 1 = 72 ✓ 72 ÷ 2 = 36 ✓ 72 ÷ 3 = 24 ✓ 72 ÷ 4 = 18 ✓ 72 ÷ 6 = 12 ✓ 72 ÷ 8 = 9 ✓ 72 ÷ 9 = 8 ✓ 72 ÷ 12 = 6 ✓ 72 ÷ 18 = 4 ✓ 72 ÷ 24 = 3 ✓ 72 ÷ 36 = 2 ✓ 72 ÷ 72 = 1 ✓
Factor pairs of 72: 1 × 72 = 72 2 × 36 = 72 3 × 24 = 72 4 × 18 = 72 6 × 12 = 72 8 × 9 = 72
Prime factorization by division method: 72 ÷ 2 = 36 36 ÷ 2 = 18 18 ÷ 2 = 9 9 ÷ 3 = 3 3 ÷ 3 = 1
Prime factorization: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
Number of factors formula: If n = p^a × q^b, then total factors = (a+1)(b+1) 72 = 2³ × 3² → factors = (3+1)(2+1) = 4 × 3 = 12 ✓
Is 72 a perfect square? No. For a perfect square, all prime factor exponents must be even. 72 = 2³ × 3² — exponent of 2 is 3 (odd) → NOT a perfect square
Is 72 a perfect cube? No. For a perfect cube, all exponents must be divisible by 3. 72 = 2³ × 3² — exponent of 3 is 2 (not divisible by 3) → NOT a perfect cube
Nearest perfect square: 64 (8²) and 81 (9²) √72 = √(36×2) = 6√2 ≈ 8.49
The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Total: 12 factors. Prime factorization: 72 = 2³ × 3².
72 = 2³ × 3² = 2 × 2 × 2 × 3 × 3. Division: 72÷2=36, 36÷2=18, 18÷2=9, 9÷3=3, 3÷3=1.
72 has 12 factors. Using the formula: 72 = 2³ × 3², so factors = (3+1)(2+1) = 12.
Factors of 15 and Prime Factorization
Learn how to find the factors of 15. Discover its prime factors, factor pairs, and understand why 15 is a composite number.
Factors of 20 and Prime Factorization
Learn how to easily calculate the factors of 20. Find out the positive and negative factor pairs and the prime factorization using a factor tree.
What are the Factors of 27?
Learn how to find all the factors of 27. See the step-by-step division method, the factor pairs, and the prime factorization of 27.
Factors of 35 and Prime Factorization
Learn how to find all the factors of 35. Discover its prime factorization and understand why it only has four factors.
What are the Factors of 54?
Learn how to calculate all the factors of 54. Understand the factor pairs, step-by-step division rules, and the prime factorization of 54.
Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.