Write all the factors of 76.

To find all the factors of 76, we need to identify every whole number that divides 76 evenly (i.e., leaves no remainder). Factors are positive integers and include 1 and the number itself. Let’s calculate them systematically:

Step-by-Step Process

• Start with 1: 76 ÷ 1 = 76 (remainder 0) → 1 and 76 are factors.
• Try 2: 76 ÷ 2 = 38 (remainder 0) → 2 and 38 are factors.
• Try 3: 76 ÷ 3 = 25.33… (not a whole number) → 3 is not a factor.
• Try 4: 76 ÷ 4 = 19 (remainder 0) → 4 and 19 are factors.
• Try 5: 76 ÷ 5 = 15.2 (not a whole number) → 5 is not a factor.
• Try 6: 76 ÷ 6 = 12.66… → 6 is not a factor.
• Try 7: 76 ÷ 7 = 10.85… → 7 is not a factor.
• Try 8: 76 ÷ 8 = 9.5 → 8 is not a factor.
• Try 9: 76 ÷ 9 = 8.44… → 9 is not a factor.
• Try 10: 76 ÷ 10 = 7.6 → 10 is not a factor.
• Check up to the square root of 76 (≈8.72): Beyond this, factors repeat as pairs.
  • 76 ÷ 19 = 4 (already found).
  • 76 ÷ 38 = 2 (already found).
  • 76 ÷ 76 = 1 (already found).

Factor Pairs

Factors come in pairs that multiply to 76:

• 1 × 76 = 76
• 2 × 38 = 76
• 4 × 19 = 76

All Factors of 76

Listing them in ascending order:
1, 2, 4, 19, 38, 76

Verification

• Total factors: 6 (an even number, typical for non-square numbers).
• Prime factorization: 76 = 2² × 19 (2 and 19 are primes), and combinations (1, 2, 4, 19, 38, 76) match.

So, the factors of 76 are: 1, 2, 4, 19, 38, 76.