Prime Time — MATHS STD 6 — Question

(a) Prime Factors of 225 and 27:
225 = 3 × 3 × 5 × 5 and 27 = 3 × 3 × 3
Since 225 contains 3 × 3 and does not have enough factors of 3 to match 3 × 3 × 3, 225 does not have sufficient factors to be divisible by 27.
Therefore, 225 is not divisible by 27.
(b) Prime Factors of 96 and 24:
96 = 2 × 2 × 2 × 2 × 2 × 3 and 24 = 2 × 2 × 2 × 3.
Since 96 includes the required factors to match those in 24, it is divisible by 24.
(c) Prime Factors of 343 and 17:
343 = 7 × 7 × 7 and 17 = 1 × 17
Since the prime factorization of 343 contains the prime factor 7 and not 17, 343 is not divisible by 17.
Thus, 343 is not divisible by 17.
(d) Prime Factors of 999 and 99: t
999 = 3 × 3 × 3 × 37 and 99 = 3 × 3 × 11
Since 999 does not include the factor 11 required for 99, 999 is not divisible by 99.