Euclid's division lemma states that given two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. This means that any positive integer a can be divided by another positive integer b, with a unique quotient q and remainder r.
We can conclude that the HCF of 980 and 78 is 2. As the remainder becomes zero, we cannot proceed further.
Euclid's Division Lemma (lemma is similar to a theorem) says that, for given two positive integers, 'a' and 'b', there exist unique integers, 'q' and 'r', such that: a = bq+r, where 0 ≤r <b. The integer 'q' is the quotient and the integer 'r' is the remainder. The quotient and the remainder are unique.
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We need to apply Euclid's Division Lemma (a = bq + r) on the given numbers, where a = 865 and b = 255. As the remainder has become 0, we can't proceed further. Now, the divisor is 5 when remainder is 0. Hence, 5 is the HCF of 865 and 255.
Since the remainder is zero and the divisor is 45, therefore, the HCF of 135 and 225 is 45. Since the remainder is zero and the divisor in this step is 195, therefore, the HCF of 38220 and 196 is 196.
Hence, H.C.F of 168 and 980 is 28.
how to do this sum by finding the hcf by long division method? by step. Since the remainder is 0, the HCF is the last divisor, which is 5. Therefore, the HCF of 65 and 135 is 5.
So, according to Euclid's Division Lemma, if we have two positive integers a and b, then there would be whole numbers q and r that satisfy the equation: a = bq + r, where 0 ≤ r < b. a is the dividend. b is the divisor. q is the quotient and r is the remainder.
Therefore, by Euclid's division lemma r must satisfy at 0 ≤ r < b. 675 = 81 × 8 + 27. The divisor is 27.
A technique of estimating the greatest common divisor of two numbers by dividing the bigger by the smaller, the lower by the remainder, the first remainder by the second remainder, and so on until actual division exists acquired thus the greatest common divisor exists the exact divisor. The HCF of 56 and 814 is 2.
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