Answer:
54 = 2×3^3
Step-by-step explanation:
Factor the following integer:
54
Hint: | Is 54 divisible by 2?
The last digit of 54 is 4, which means it is even. Therefore 54 is divisible by 2:
54 = 2 27:
54 = 2×27
Hint: | Now try to factor 27. Is 27 divisible by 2?
27 is not divisible by 2 since 27 is odd and 2 is even:
54 = 2×27 (27 is not divisible by 2)
Hint: | Is 27 divisible by 3?
The sum of the digits of 27 is 2 + 7 = 9, which is divisible by 3. This means 27 is divisible by 3:
27 = 3 9:
54 = 2×3×9 (9 is not divisible by 2 since 27 is not)
Hint: | Now try to factor 9. Is 9 divisible by 3?
9 = 3 3, which means 9 is divisible by 3:
9 = 3 3:
54 = 2×3×3×3 (3 is not divisible by 2 since 9 is not)
Hint: | Now try to factor 3. Is 3 prime?
No primes less than 3 divide into it. Therefore 3 is prime:
54 = 2×3×3×3
Hint: | Express 54 as a product of prime powers.
There is 1 copy of 2 and 3 copies of 3 in the product:
Answer: 54 = 2×3^3
