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Question

# Using Euclid’s division Lemma for any natural number and 4, which of the following forms can a positive integer be represented as, where m is an integer?

A

4m

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B

4m + 1

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C

4m + 2

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D
All of the above.
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Solution

## The correct option is D All of the above.Let n be an arbitrary positive integer On dividing n by 4, let m be the quotient and r be the remainder. Then, by Euclid’s Division Lemma, we have n = 4m + r , where 0≤r<4 n = 4m , n = 4m + 1 , n = 4m + 2 and n = 4m + 3 for some integer m. Thus, all the options are true.

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