Question

EXERCISE 1.11. Use Euclid's division algorithm to find the HCF of:(1) 135 and 225(ii) 196 and 38220(iii) 867 and 2552. Show that any positive odd integer is of the form 6q+1, or 69 +3, or 69 +5, where q issome integer3. An army contingent of 616 members is to march behind an army band of 32 members ina parade. The two groups are to march in the same number of columns. What is themaximum number of columns in which they can march?4. Use Euclid's division lemma to show that the square of any positive integer is either ofthe form 3m or 3m + 1 for some integer m.[Hint: Letxbe any positive integer then it is of the form 37, 39 +1 or 34 +2. Now squareeach of these and show that they can be rewritten in the form 3m or 3m + 1.5. Use Euclid's division lemma to show that the cube of any positive integer is of the form9m, 9m + 1 or 9m +8.​

Answer 1

Answer:

Euclid division algorithm

1. 1) 225=135*1+90

135=90*1+45

90=45*2+0

HCF is 45

2) 38220=196*195+0

HCF is 196

3) 867=255*3+102

255= 102*2+51

102=51*2+0

HCF is 51