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Standard X

Mathematics

Euclid's Division Lemma

A positive in...

Question

A positive integer a is written as a=3q+r and a=4k+r , where q,k and r are whole numbers. Find possibilities of q and k

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Solution

1. a = 3q + r
that is 3q + r - a = 0
2. a = 4k + r
That is 4k + r - a = 0

subtract first equation from second equation
4k - 3q = 0
4k = 3q

k/q = 3/4
possibilities of k and q is any whole number whose ratio is 3/4.

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A positive integer a is written as a=3q+r and a=4k+r , where q,k and r are whole numbers. Find possibilities of q and k

1. a = 3q + r that is 3q + r - a = 0 2. a = 4k + r That is 4k + r - a = 0 subtract first equation from second equation 4k - 3q = 0 4k = 3q k/q = 3/4 possibilities of k and q is any whole number whose ratio is 3/4.

1. a = 3q + r
that is 3q + r - a = 0
2. a = 4k + r
That is 4k + r - a = 0

subtract first equation from second equation
4k - 3q = 0
4k = 3q

k/q = 3/4
possibilities of k and q is any whole number whose ratio is 3/4.