[Solved] Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8. Solutions: Let ‘a’ be any positive integer and b = 3.∴ By Euclid’s division algorithm, we have a = bq + r,0 ≤ r ≤ ba = 3q + r,0 …

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[Solved] An army contingent of 616 members is to march behind an army band of 32 members in a parade.

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Solution: Maximum number of columns = HCF of (616, 32)For finding the …

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[Solved] Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. Solution: Let ‘a’ be any positive integer and b = 6.∴ By Euclid’s division algorithm, we havea = bq + r, 0 ≤ r ≤ ba = 6q + …

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[Solved] Use Euclid’s division algorithm to find the HCF of 867 and 255.

Use Euclid’s division algorithm to find the HCF of 867 and 255. Solution: Given numbers are 867 and 255By applying Euclid’s division algorithm, we have867 = 255 x 3 + 102Since the remainder is 102 ≠ 0, so again we apply Euclid’s division algorithm to 255 and 102. to get255 = 102 x 2 + …

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[Solved] Use Euclid’s division algorithm to find the HCF of 196 and 38220.

Use Euclid’s division algorithm to find the HCF of 196 and 38220. Solution: Given numbers are 196 and 38220By applying Euclid’s division algorithm, we have38220 = 196 x 195 + 0Since we get the remainder zero in the first step, so we stop.∵ At the above stage, the divisor is 196∴ The HCF of 196 …

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[Solved] Use Euclid’s division algorithm to find the HCF of 135 and 225.

Use Euclid’s division algorithm to find the HCF of 135 and 225. Solution: Given numbers are 135 and 225.By applying Euclid’s division algorithm, we have225 = 135 x 1 + 90Since the remainder is 90 ≠ 0, so again we apply Euclid’s division algorithm to 135 and 90, to get135 = 90 x 1 + …

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