Find the LCM and HCF of the following integers by applying the prime factorisation method. (iii) 8, 9 and 25
(iii) 8, 9 and 25
Now, 8 = 2 × 2 × 2 = 23,
9 = 3 × 3 = 32
and 25 = 5 × 5 = 52
Since, there is no smallest common factor.
∴ H.C.F. (8, 9, 25) = 1.
And 23, 32, and 52 are greatest powers of prime factors.
∴ L.C.M. (8, 9, 25) = 23 × 32 × 52 = 1800.
Use Euclid’s division algorithm to find the HCF of:
(i)135 and 225 (ii) 196 and 38220.
Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
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?
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.
Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.
Express each number as a product of its prime factors: (i) 140
Express each number as a product of its prime factors: (ii) 156
Express each number as a product of its prime factors: (ii) 156 (iii) 3825 (iv) 5005 (v) 7429
Express each number as a product of its prime factors: (iv) 5005
Express each number as a product of its prime factors: (v) 7429
Mock Test Series
