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Question

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Use Euclid’s division to find HCF of 126 and 1078.

Solution

Given integers are 126 and 1078. Clearly 1078 > 126.
Therefore, by applying Euclid’s division lemma to 126 and 1078, we get

II. Since, the remainder 70 ≠ 0, we apply division lemma to 70 and 126 to get

III. We consider the new divisor 70 and new remainder 56 and apply division lemma to get

IV. We consider the new divisor 56 and new remainder 14 and apply division lemma to get

Some More Questions From Real Numbers Chapter

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Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

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Express each number as a product of its prime factors: (i) 140

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Express each number as a product of its prime factors: (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

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Express each number as a product of its prime factors: (v) 7429

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91

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