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consider the number 4^n, where n …

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consider the number 4^n, where n is a natural number. Check whether there is any value of n for which 4^n ends with the digit zero

Posted by Debarshi Maity 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 7 months ago

If the number 4n, for any n, were to end with the digit zero, then it would be divisible by 5. That is, the prime factorisation of 4n would contain the prime 5. This is not possible because 4ⁿ = (2)²ⁿ; so the only prime in the factorisation of 4ⁿ is 2. So, the uniqueness of the Fundamental Theorem of Arithmetic guarantees that there are no other primes in the factorisation of 4ⁿ. So, there is no natural number n for which 4ⁿ ends with the digit zero.
You have already learnt how to find the HCF and LCM of two positive integers using the Fundamental Theorem of Arithmetic in earlier classes, without realising it! This method is also called the prime factorisation method. Let us recall this method through an example.

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Posted by Hari Anand 7 months, 1 week ago

CBSE > Class 10 > Mathematics

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This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

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Posted by Kanika . 2 months ago

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