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Check whether 6 can end with the digit 0 for any natural number n

Posted by Soni ? 4 years, 6 months ago

CBSE > Class 10 > Mathematics

3 answers

Soni ? 4 years, 6 months ago

Thank you

0Thank You

Adithya Dev A 4 years, 6 months ago

If 6^n is to end with zero (where n is a natural number), it has to be a multiple of 5. That is 6^n should have a prime factor 5. However, this number can only be written as 2^3n or 3^2n so, 5is not there in the prime factorisation. Therefore, the uniqueness of the fundamental theorem of arithmetic guarantees that 5 cannot be a factor of the number. So, 6^n cannot end with 0.

1Thank You

Soni ? 4 years, 6 months ago

Plz give me answer and explain this plz

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