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For determining last digit of a power for numbers 0, 1, 5, and 6, I am not clear on how to determine the last digit.

Your post says: • Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base.

What is the last digit of 345^27 ---is the last digit 5? What is the last digit of 216^32----is the last digit 6? What is the last digit of 111^56---is the last digit 1?

For determining last digit of a power for numbers 0, 1, 5, and 6, I am not clear on how to determine the last digit.

Your post says: • Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base.

What is the last digit of 345^27 ---is the last digit 5? What is the last digit of 216^32----is the last digit 6? What is the last digit of 111^56---is the last digit 1?

Any clarification would be helpful.

Thanks for all your help.

First of all: last digit of 345^27 is the same as that of 5^27 (the same for 216^32 and 111^56);

Next: 1 in any integer power is 1; 5^1=5, 5^2=25, 5^3=125, ... 6^1=6, 6^2=36, 5^3=216, ...

So yes, integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base: thus 0, 1, 5, and 6 respectively.

I am having a small confusion between two concepts for which one of my practice Q went wrong. During my elementary school I have studied BODMAS B - Brackets O - Of D- Division M-Mulitplication A- Addition S- Substraction

I tried with this approach and it went wrong, while i was going through this again i happened to see a difference between PEMDAS & BODMAS (Multiplication order is different) .

Can somebody help me to understand which one i should follow.

I am having a small confusion between two concepts for which one of my practice Q went wrong. During my elementary school I have studied BODMAS B - Brackets O - Of D- Division M-Mulitplication A- Addition S- Substraction

I tried with this approach and it went wrong, while i was going through this again i happened to see a difference between PEMDAS & BODMAS (Multiplication order is different) .

Can somebody help me to understand which one i should follow.

Thanks Humble GMAT ASPIRANT

The rule mentioned in the initial post is correct.

Anyway: what difference are you talking about? Can you give an example?
_________________

Any nonzero natural number n can be factored into primes, written as a product of primes or powers of primes. Moreover, this factorization is unique except for a possible reordering of the factors.

Pls give me the example of bold face text because i am not sure what does it exactly means.

Thanks
_________________

The proof of understanding is the ability to explain it.

Any nonzero natural number n can be factored into primes, written as a product of primes or powers of primes. Moreover, this factorization is unique except for a possible reordering of the factors.

Pls give me the example of bold face text because i am not sure what does it exactly means.

Thanks

It's called the fundamental theorem of arithmetic (or the unique-prime-factorization theorem) which states that any integer greater than 1 can be written as a unique product of prime numbers.

For example: 60=2^2*3*5 --> 60 can be written as a product of primes (powers of primes) only in this unique way (you can just reorder the multiples and write 3*2^2*5 or 2^2*5*3 ...).
_________________

thank you for the great post. I currently use the GMAT Toolkit app, which I highly recommend, when can I expect this update? In addition, when will the Manhattan GMAT books be updated to the app?

Thanks,

gmatclubot

Re: Math: Number Theory
[#permalink]
27 May 2011, 07:21

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