Math, asked by Ashutosh200, 10 months ago

show that any number of the form 6x, x belong to n can never end with digit 0.

Answers

Answered by saivivek16

Hey mate,.

Let 6x ends with digit 0 .

Hence 5 must be a factor of 6x

Which is not possible because the prime factorisation of 6x is (2×3)n

The fundamental theorem of arithmetic guarantees that there is no other primes in the prime factorisation of 6x .so there is no natural number n for which 6x ends with digit 0.as to be the digit ending with 0 it must be a factor of 10 which is not possible in the case of the prime factorisation of 6x as it comprises of 2 and 3 but not 5.

Hope it will help you.

✨sai

sivaprasath: bro, if x = 10, 6x = 60 , which ends with 0

saivivek16: I had taken 6=(2×3)

sivaprasath: ya, but you need to prove 6x will never end with 0, when n ∈ N ??

sivaprasath: what if x is a factoor of 5 ??

sivaprasath: factor*

Answered by Nєєнα

Step-by-step explanation:

prime factorisation of 6^n = (2×3)^n

it contains "2" in prime factorisation but it lacks "5" in it

it is not divisible by 2 , 5 both and 10

so it is not possible to for the number to end with zero if it is not divisible by 10

hope it helps u.....❣️

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