Answer:
-110 = -2^1×5^1×11^1
Explanation:
Factor the following integer:
-110
Hint: | Is 110 divisible by 2?
The last digit of 110 is 0, which means it is even. Therefore 110 is divisible by 2:
110 = 2 55:
-110 = -2×55
Hint: | Now try to factor 55. Is 55 divisible by 2?
55 is not divisible by 2 since 55 is odd and 2 is even:
-110 = -2×55 (55 is not divisible by 2)
Hint: | Is 55 divisible by 3?
The sum of the digits of 55 is 5 + 5 = 10, which is not divisible by 3. This means 55 is not divisible by 3:
-110 = -2×55 (55 is not divisible by 2 or 3)
Hint: | Is 55 divisible by 5?
The last digit of 55 is 5, which means 55 is divisible by 5:
55 = 5 11:
-110 = -2×5×11 (11 is not divisible by 2 or 3 since 55 is not)
Hint: | Now try to factor 11. Is 11 divisible by 5?
The last digit of 11 is not 5 or 0, which means 11 is not divisible by 5:
-110 = -2×5×11 (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:
-110 = -2×5×11 (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:
-110 = -2×5×11
Hint: | Express -110 as a product of prime powers.
There is 1 copy of 2, 1 copy of 5 and 1 copy of 11 in the product:
Answer: -110 = -2^1×5^1×11^1