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Let n be a positive integer which when divided by 6 gives quotient q and remainder r.
Using Euclid Division lemma,
n= 6q +r where possible r= 0,1,2,3,4 and 5.
Case 1-
let r=0 , n = 6q (which is even)
Case 2-
let r=1 , n = 6q +1 (which is odd)
Case 3 -
let r = 2 , n = 6q + 2 (which is even)
Case 4-
let r=3 , n= 6q+ 3 (which is odd)
Case 5-
let r=4, n = 6q+ 4 (which is even)
Case 6-
let r=5 , n = 6q+ 5 (which is odd)
Hence,an even integer is of the form 6q or 6q+2 or 6q+4.
Hope it helps!
Using Euclid Division lemma,
n= 6q +r where possible r= 0,1,2,3,4 and 5.
Case 1-
let r=0 , n = 6q (which is even)
Case 2-
let r=1 , n = 6q +1 (which is odd)
Case 3 -
let r = 2 , n = 6q + 2 (which is even)
Case 4-
let r=3 , n= 6q+ 3 (which is odd)
Case 5-
let r=4, n = 6q+ 4 (which is even)
Case 6-
let r=5 , n = 6q+ 5 (which is odd)
Hence,an even integer is of the form 6q or 6q+2 or 6q+4.
Hope it helps!
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