Question 28 of 36intermediate🔧 ApplyNumerical4 marks
Is the first number divisible by the second? Use prime factorisation. a. 225 and 27 b. 96 and 24 c. 343 and 17 d. 999 and 99
(a)
Is 225 divisible by 27?
Answer
No, 225 is not divisible by 27.
(b)
Is 96 divisible by 24?
Answer
Yes, 96 is divisible by 24.
(c)
Is 343 divisible by 17?
Answer
No, 343 is not divisible by 17.
(d)
Is 999 divisible by 99?
Answer
No, 999 is not divisible by 99.
Explanation
(a) 225 = 3² × 5² and 27 = 3³. The prime factorisation of 27 (3³) is not included in 225 (which has only 3²). (b) 96 = 2⁵ × 3 and 24 = 2³ × 3. The prime factorisation of 24 is included in 96. (c) 343 = 7³ and 17 = 17. The prime factor 17 does not appear in the prime factorisation of 343. (d) 999 = 3³ × 37 and 99 = 3² × 11. The prime factor 11 does not appear in the prime factorisation of 999.