Concept: HCF using Euclid's Division Algorithm
Use Euclid’s division algorithm to find the HCF of:
- 135 and 225
- 196 and 38220
- 867 and 255
Concept: Euclid's Lemma on n and 6
Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
Concept: Word Problem on HCF
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?
Concept: Euclid's Division Lemma : n2 and 3
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.
Concept: Euclid's Division Lemma : n3 and 3
Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.
