Find all the factors of 27.

To find all the factors of 27, we need to identify every whole number that divides 27 evenly (i.e., leaves no remainder). Factors are positive integers and include 1 and the number itself. Let’s determine them systematically:

Step-by-Step Process

• Start with 1: 27 ÷ 1 = 27 (remainder 0) → 1 and 27 are factors.
• Try 2: 27 ÷ 2 = 13.5 (not a whole number) → 2 is not a factor.
• Try 3: 27 ÷ 3 = 9 (remainder 0) → 3 and 9 are factors.
• Try 4: 27 ÷ 4 = 6.75 → 4 is not a factor.
• Try 5: 27 ÷ 5 = 5.4 → 5 is not a factor.
• Try 6: 27 ÷ 6 = 4.5 → 6 is not a factor.
• Try 7: 27 ÷ 7 = 3.857… → 7 is not a factor.
• Try 8: 27 ÷ 8 = 3.375 → 8 is not a factor.
• Try 9: 27 ÷ 9 = 3 (already found) → confirms 9 and 3.
• Check up to the square root of 27 (≈5.196): Beyond this, factors repeat as pairs.
  • 27 ÷ 27 = 1 (already found).

Factor Pairs

Factors come in pairs that multiply to 27:

• 1 × 27 = 27
• 3 × 9 = 27

All Factors of 27

Listing them in ascending order:
1, 3, 9, 27

Verification

• Total factors: 4 (even, typical for non-square numbers with prime factorization).
• Prime factorization: 27 = 3³ (3 is prime), and combinations (1, 3, 9, 27) match:
  • 3⁰ = 1
  • 3¹ = 3
  • 3² = 9
  • 3³ = 27

So, the factors of 27 are: 1, 3, 9, 27.