Factors of 72

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. A factor is a whole number that divides 72 exactly without leaving a remainder. These factors can be used to simplify fractions, solve math problems, and understand number relationships.

To find the factors of 72, divide the number by whole numbers starting from 1. If the result is a whole number with no remainder, that divisor is a factor.

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

A number is divisible by another number if the division leaves no remainder.

✅ 72 is divisible by 2
✅ 72 is divisible by 3
✅ 72 is divisible by 4
❌ 72 is not divisible by 5
✅ 72 is divisible by 6
❌ 72 is not divisible by 7
✅ 72 is divisible by 8
✅ 72 is divisible by 9
❌ 72 is not divisible by 10

Factors of 72 are useful in mathematics, grouping objects, simplifying fractions, finding dimensions of rectangles, and solving division problems. Understanding factors helps students build a strong foundation in arithmetic and number theory.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

• 1 × 72
• 2 × 36
• 3 × 24
• 4 × 18
• 6 × 12
• 8 × 9

72 = 2 × 2 × 2 × 3 × 3

Step 1: Start testing numbers from 1 up to 72.

Step 2: Check which numbers divide 72 without leaving a remainder.

Step 3: The successful divisions are:

72 ÷ 1 = 72 (No remainder)
72 ÷ 2 = 36 (No remainder)
72 ÷ 3 = 24 (No remainder)
72 ÷ 4 = 18 (No remainder)
72 ÷ 6 = 12 (No remainder)
72 ÷ 8 = 9 (No remainder)
72 ÷ 9 = 8 (No remainder)
72 ÷ 12 = 6 (No remainder)
72 ÷ 18 = 4 (No remainder)
72 ÷ 24 = 3 (No remainder)
72 ÷ 36 = 2 (No remainder)
72 ÷ 72 = 1 (No remainder)

Answer: Therefore, the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Even or Odd: Even Number

Prime or Composite: Composite Number

Perfect Square: No

Perfect Cube: No

Unique Prime Factors: 2, 3

• 72 is a composite number because it has more than two factors.
• 72 is an even number.
• The prime factorization of 72 is 2 × 2 × 2 × 3 × 3.
• 72 has 12 total factors.

72 is a composite number because it has 12 factors.

What are the factors of 72?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

How many factors does 72 have?
12

Is 72 a prime number?
No

What is the largest factor of 72?
72

What is the smallest factor of 72?
1

What are the prime factors of 72?
2, 3

Is 72 even or odd?
Even

What is the factor pair of 72?
1 × 72, 2 × 36, 3 × 24, 4 × 18, 6 × 12, 8 × 9