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