7. Factor the expression.
42 - 64

-22 = -2^1×11^1

Step-by-step explanation:

Factor the following integer:

-22

Hint: | Is 22 divisible by 2?

The last digit of 22 is 2, which means it is even. Therefore 22 is divisible by 2:

22 = 2 11:

-22 = -2×11

Hint: | Now try to factor 11. Is 11 divisible by 2?

11 is not divisible by 2 since 11 is odd and 2 is even:

-22 = -2×11 (11 is not divisible by 2)

Hint: | Is 11 divisible by 3?

The sum of the digits of 11 is 1 + 1 = 2, which is not divisible by 3. This means 11 is not divisible by 3:

-22 = -2×11 (11 is not divisible by 2 or 3)

Hint: | Is 11 divisible by 5?

The last digit of 11 is not 5 or 0, which means 11 is not divisible by 5:

-22 = -2×11 (11 is not divisible by 2, 3 or 5)

Hint: | Is 11 divisible by 7?

Divide 7 into 11:

| | 1 | (quotient)

7 | 1 | 1 |  

- | | 7 |  

| | 4 | (remainder)

11 is not divisible by 7:

-22 = -2×11 (11 is not divisible by 2, 3, 5 or 7)

Hint: | Is 11 prime?

No primes less than 11 divide into it. Therefore 11 is prime:

-22 = -2×11

Hint: | Express -22 as a product of prime powers.

There is 1 copy of 2 and 1 copy of 11 in the product:

-22 = -2^1×11^1