Factor the following integer: 78 The last digit of 78 is 8, which means it is even. Therefore 78 is divisible by 2: 78 = 2 39: 78 = 2×39 39 is not divisible by 2 since 39 is odd and 2 is even: 78 = 2×39 (39 is not divisible by 2) The sum of the digits of 39 is 3 + 9 = 12, which is divisible by 3. This means 39 is divisible by 3:
39 = 3 13: 78 = 2×3×13 (13 is not divisible by 2 since 39 is not)
The sum of the digits of 13 is 1 + 3 = 4, which is not divisible by 3. This means 13 is not divisible by 3: 78 = 2×3×13 (13 is not divisible by 2 or 3) The last digit of 13 is not 5 or 0, which means 13 is not divisible by 5: 78 = 2×3×13 (13 is not divisible by 2, 3 or 5) Divide 7 into 13: | | 1 7 | 1 | 3 - | | 7 | | 6 13 is not divisible by 7: 78 = 2×3×13 (13 is not divisible by 2, 3, 5 or 7) The alternating sum of the digits of 13 is 1 - 3 = -2, which is not divisible by 11. This means 13 is not divisible by 11: 78 = 2×3×13 (13 is not divisible by 2, 3, 5, 7 or 11) No primes less than 13 divide into it. Therefore 13 is prime: 78 = 2×3×13 There is 1 copy of 2, 1 copy of 3 and 1 copy of 13 in the product: Answer: 78 = 2×3×13
