SOLUTION: smallest natural number of 535392 forms a perfect square! Thanks!

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Question 828384: smallest natural number of 535392 forms a perfect square!
Thanks!

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Smallest natural number what of 535392 forms a perfect square? Smallest number made with the digits of 535392? Smallest factor of 535392?

The interesting question would be
"What is the smallest multiple of 535392 which is a perfect square?"

Dividing the number by prime factors in order we can get the prime factorization of 535392.
535392 ÷ 2 = 267696
267696 ÷ 2 =133848
133848 ÷ 2 = 66924
66924 ÷ 2 = 33462
33462 ÷ 2 = 16731
16731 ÷ 3 = 5577
5577 ÷ 3 = 1859
1859 ÷ 11 = 169
169 ÷ 13 = 13
13 ÷ 13 = 1
So 535392=2%2A2%2A2%2A2%2A2%2A3%2A3%2A11%2A13%2A13=2%5E5%2A3%5E2%2A11%2A13%5E2
To be a perfect square the factor must come in pairs,
and the smallest multiple that is a perfect square is