Question

(1) When a is divided by b according to division lemma it is, a = b c, (a) What is H.C.F. of a and b? (b) What is H.C.F. of a and c? (2) When a is divided by b according to division lemma it is, a = b q + r b = y r What is H.C.F. of a and b? Why?​

Answer 1

Answer:

I think your question is incomplete

Step-by-step explanation:

so write your full answer

Answer 2

The correct question is, " When a is divided by b according to the division lemma it is, a = b × c,

(a) What is H.C.F. of a and b?

(b) What is H.C.F. of a and c?

(2) When a is divided by b according to the division lemma it is,

a = b×q+r

b = y × r

What is H.C.F. of a and b? Why?​

The answers are b,c, and r.

Given:

$a=b*c$

$a=b*q+r$

$b=y*r$

To Find:

1)The H.C.F of a and b

2)The H.C.F of a and c

3) The H.C.F of a and b

Solution :

A number can be written as $x=Q*y+r$, where Q is the quotient, and r is the remainder.

1) As given, when a is divided by b, the remainder is 0. Therefore a is divisible by b. Hence the H.C.F of a and b will be b.

2) Similarly, when a is divided by c, the remainder is 0. Therefore a is divisible by c. Hence the H.C.F of a and c will be c.

3) As given, when b is divided by r, the remainder is zero. Hence b is divisible by r. Therefore the H.C.F of b and r is r.

$a=bq +r\\b= yr\\a=yqr+r\\a=r[yq+1]$

Hence we can see a is also divisible by r, therefore the H.C.F of a and r is also r. Therefore as both a and be have H.C.F r with r, the H.C.F of a and b is also r.

The H.C.F of a and b is b, the H.C.F of a and c is c, and the H.C.F of a and b is r.

#SPJ3