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Factor 2X4 - 20x2 - 78.

User Hiba
by
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1 Answer

7 votes

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

User Jogendar Choudhary
by
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