Proof of divisibility of 6

Question

How to prove that if a number is divisible by 2 and 3 both,it is also divisible by 6.It should be proven by using Euclid's Division Lemma.

@Dietrich, Not really a duplicate of that question because the OP says the answer must use Euclid's Division Lemma. — lhf, May 05 '20 at 11:41

score 1 · Answer 1 · answered May 05 '20 at 11:46

1

Hint:

Assume $2|m$, then $m=2k;$

Assume $3|m$ then $3|2k$.

Now use Euclid's lemma.

answered May 05 '20 at 11:46

Peter Szilas

20,344
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score 0 · Accepted Answer · answered May 05 '20 at 11:39

0

Hint: Write $n=6q+r$ with $0 \le r \le 5$. Since $n$ is divisible by $2$, so is $r$. Since $n$ is divisible by $3$, so is $r$. What $r$ are possible?

answered May 05 '20 at 11:39

lhf

216,483

Proof of divisibility of 6

2 Answers2