Check whether 6^n and 15^n can end with the digit zero.
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!! Hey Mate !!
your answer is ---
◆ if 6^n end with digit zero then 6^n must be divisible by 2 and 5
it means 2 and 5 is must be a prime factor of 6^n.
but , 6^n = (2×3)^n = 2^n × 3^n
so, there is no prime 5 as a factor of 6^n
therefore , 6^n can't end with digit zero .
◆ if 15^n end with digit zero then it must be divisible by 2 and 5
as 2×5 = 10
it means 15^n must contain 2 and 5 as a prime factor
but 15^n = 3^n × 5^n
so, prime factor of 15^n doesn't contain 2 as a prime
therefore , 15^n can't end with digit zero
HOPE IT HELPS YOU
your answer is ---
◆ if 6^n end with digit zero then 6^n must be divisible by 2 and 5
it means 2 and 5 is must be a prime factor of 6^n.
but , 6^n = (2×3)^n = 2^n × 3^n
so, there is no prime 5 as a factor of 6^n
therefore , 6^n can't end with digit zero .
◆ if 15^n end with digit zero then it must be divisible by 2 and 5
as 2×5 = 10
it means 15^n must contain 2 and 5 as a prime factor
but 15^n = 3^n × 5^n
so, prime factor of 15^n doesn't contain 2 as a prime
therefore , 15^n can't end with digit zero
HOPE IT HELPS YOU
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