for positive integers 'a' and 'b',a=bq+0,than HCF of 'a'and 'b'is?
Answers
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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Learn more from Brainly :-
1. If HCF of two numbers be 40 then which of the following cannot be their LCM.
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2. The HCF and LCM of two numbers are 17 & 1666 respectively. if one of the numbers is 119 find the other
Step-by-step explanation:
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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