Answer:
-25677 = -3^4×317^1
Step-by-step explanation:
Factor the following integer:
-25677
Hint: | Show that 25677 is divisible by 9.
The sum of the digits of 25677 is 2 + 5 + 6 + 7 + 7 = 27, which is divisible by 9. This means 25677 is too
25677 = 9×2853:
-25677 = -9×2853
Hint: | Express 9 as a square.
9 = 3^2:
-25677 = -3^2×2853
Hint: | Show that 2853 is divisible by 9.
The sum of the digits of 2853 is 2 + 8 + 5 + 3 = 18, which is divisible by 9. This means 2853 is too
2853 = 9×317:
-25677 = -3^2×9×317
Hint: | Express 9 as a square.
9 = 3^2:
-25677 = -3^2×3^2×317
Hint: | 3 has no proper divisors.
3 is prime:
-25677 = -3^2×3^2×317
Hint: | Find a divisor of 317 by testing the integers between 2 and sqrt(317)≈17.8 for divisibility.
Because 317 is odd, only test odd numbers for divisibility
317 is not divisible by 3, 5, 7, 9, 11, 13, 15 or 17
Since 317 is not divisible by any integer up to 17, it is prime:
-25677 = -3^2×3^2×317
Hint: | Express -25677 as a product of prime powers.
There are 4 copies of 3 and 1 copy of 317 in the product:
Answer: -25677 = -3^4×317^1
