Math, asked by irfannatha4506, 2 months ago

for positive integers 'a' and 'b',a=bq+0,than HCF of 'a'and 'b'is?​

Answers

Answered by patelbhavya20
0

Answer:

a and b are positive integers, then you know that a = bq + r, such that 0 ≤ r ≤ b , where q is a whole number.

TO PROVE

HCF(a,b) = HCF(b, r)

PROOF

Let c = HCF(a,b) & d = HCF(b, r)

Since c = HCF(a,b)

⟹ c divides a and c divides b

⟹ c divides a and c divides bq

⟹ c divides a - bq

⟹ c divides r

⟹ c is a common divisor of b & r

⟹ c divides d

Similarly we can show that d divides c

Now c and d are positive integers

Consequently c = d

Hence HCF(a,b) = HCF(b, r)

Hence proved

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Answered by krishna4646
0

Answer:

If a and b are any two positive integers then HCF(a, b) × LCM(a, b) is equal to

Top answer · 4 votes

There is an identity which holds for all integers: LCM(a,b) × HCF(a,b) = ab More

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