What is the smallest number by which 2880 must be divided in order to make it…
2023
What is the smallest number by which 2880 must be divided in order to make it into a perfect square?
- A.
3
- B.
4
- C.
5
- D.
6
Attempted by 27 students.
Show answer & explanation
Correct answer: C
Key idea: all prime exponents must be even for a number to be a perfect square.
Prime factorization: 2880 = 2^6 × 3^2 × 5^1
Check exponents: 2 has exponent 6 (even), 3 has exponent 2 (even), 5 has exponent 1 (odd).
Remove the unpaired prime by dividing by 5 to make its exponent zero: result = 2^6 × 3^2 = 64 × 9 = 576.
Since 576 = 24^2, the quotient is a perfect square.
Therefore the smallest number by which 2880 must be divided to become a perfect square is 5.