FIND THE LEAST NUMBER BY WHICH 21168 MUST BE DIVIDED IN ORDER TO YIELD A PERFECT SQUARE ?
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To find the least number by which 21168 must be divided in order to yield a perfect square, we need to factorize 21168 and analyze its prime factors.
First, let's factorize 21168:
21168 = 2^4 * 3^3 * 31
Now, we need to look at the prime factors and their exponents. In order to form a perfect square, each prime factor's exponent must be an even number.
Looking at the exponents:
- The exponent of 2 is 4, which is already an even number.
- The exponent of 3 is 3, which is an odd number.
To make the exponent of 3 even and create a perfect square, we need to divide 21168 by an additional factor of 3. This will reduce the exponent of 3 from 3 to 2, which is an even number.
Therefore, the least number by which 21168 must be divided in order to yield a perfect square is 3.
Dividing 21168 by 3:
21168 / 3 = 7056
7056 is the least number that can be obtained by dividing 21168 and results in a perfect square.
21168
= 4x4x4x9x147
since 147 is prime
21168 ÷ 147 = 144 which is a perfect square
Find the least number by which 21168 must be divided in order to yeild a perfect square
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