Question

Exercise- 8.4
Use multiplication to find the factors of:
a. 151,3,5,15 b. 201,2,4,5), 2. 24
d. 28
e. 32
f. 45
2 Use division to find the factors of:
b. 18
c. 36
a. 12
d. 54
f. 81
e. 63
3. Find the HCF of the following numbers:
b. 10,20
c. 15, 20
d. 40,48
a. 8,12
f. 9, 12
8. 16, 24,32
h. 22,14,18
e. 16, 12
4. Write true (T) or false (F):
a. 4 is a factor of 48.
b. 10 is a factor of 25.​

Answer 1

Answer:

Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r, for some integer q ≥ 0, and r = 0, 1, 2, 3, 4, 5, because 0≤r<6.

Now substituting the value of r, we get,

If r = 0, then a = 6q

Similarly, for r= 1, 2, 3, 4 and 5, the value of a is 6q+1, 6q+2, 6q+3, 6q+4 and 6q+5, respectively.

If a = 6q, 6q+2, 6q+4, then a is an even number and divisible by 2. A positive integer can be either even or odd Therefore, any positive odd integer is of the form of 6q+1, 6q+3 and 6q+5, where q is some integer.

3. 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