Multiple choice

If M = 77 $\times$ 144 $\times$ 45, which of the following groups gives the prime factors of M?

  1. 2, 3, 5, 7, 11, 13

  2. 2, 3, 5, 19

  3. 2, 3, 5, 7, 11, 13, 14

  4. 2, 3, 5, 7, 11
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

M = 77 $\times$ 144 $\times$ 45 = 7 $\times$ 11 $\times$ 12 $\times$ 12 $\times$ 9 $\times$ 5 = 7 $\times$ 11 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 3 $\times$ 5 So, prime factors of M are 2, 3, 5, 7 and 11.

AI explanation

Breaking each factor into primes: 77 = 7 x 11, 144 = 2^4 x 3^2, and 45 = 3^2 x 5. Combining all of these, the complete set of distinct prime factors of M is 2, 3, 5, 7, and 11 - no other primes appear in any of the three numbers.

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