Question

the total number of prime factors of (7 x 2)24 x (4 x 5)21 is :

Answer 1

Answer:

$\bold{3}$

Step-by-step explanation:

$(7 \times 2)^{24} \times (4 \times 5)^{21} \\ \\ = (7 \times 2)^{24} \times (2 \times 2 \times 5)^{21} \\ \\ = 7^{24} \times 2^{24} \times 2^{21} \times 2^{21} \times 5^{21} \\ \\ = 7^{24} \times 2^{24 + 21 + 21} \times 5^{21} \\ \\ = 7^{24} \times 2^{66} \times 5^{21}$

$\\ \\ \\ \therefore\ (7 \times 2)^{24} \times (4 \times 5)^{21} = 7^{24} \times 2^{66} \times 5^{21} \\ \\ \\ \therefore\ (7 \times 2)^{24} \times (4 \times 5)^{21}\ has\ \bold{3}\ prime\ factors,\ and\ those\ are\ 2,\ 5\ and\ 7.$

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