How do you work out what times what 176?

Answer 1

I always start with the prime factorization. That's 2^4 x 11. Adding one to the exponents and multiplying them tells me that 176 has 10 factors. Half of them will be less than the square root, half greater. The square root of 176 is between 13 and 14. We know that 1 is a factor because 1 is a factor of everything. We know that 2 is a factor because it's even. We know that 11 is a factor from the prime factorization. So we're looking for two factors between 2 and 11. From the rules of divisibility we know that 3, 5, 9 and 10 aren't factors. So we test 4, 6, 7 and 8. 4 and 8 qualify.

Divide 1, 2, 4, 8 and 11 into 176.

The factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176