The number of prime factors of 3 - 5122 - 7101025 is

The correct option is D 4 (3× 5) ^ 12 × (2× 7) ^ 10 × 10 ^ 25 = 2 ^ 35 × 3 ^ 12 × 5 ^ 37 × 7 ^ 10 Therefore, number of prime factors is equal to #1 ...

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Standard X

Mathematics

Fundamental Theorem of Arithmetic

The number of...

Question

The number of prime factors of $(3 \times 5)^{12} (2 \times 7)^{10} (10)^{25}$ is

94

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6

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47

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4

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Solution

The correct option is D $4$
${(3 \times 5)}^{12} \times {(2 \times 7)}^{10} \times 10^{25} = 2^{35} \times 3^{12} \times 5^{37} \times 7^{10}$
Therefore, number of prime factors is equal to $4$ , i.e., ${2, 3, 5, 7}$

Hence, option D.

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The number of prime factors of (3×5)12(2×7)10(10)25 is

The correct option is D 4(3×5)12×(2×7)10×1025=235×312×537×710Therefore, number of prime factors is equal to 4, i.e., {2,3,5,7}Hence, option D.

The number of prime factors of $(3 \times 5)^{12} (2 \times 7)^{10} (10)^{25}$ is

The correct option is D $4$
${(3 \times 5)}^{12} \times {(2 \times 7)}^{10} \times 10^{25} = 2^{35} \times 3^{12} \times 5^{37} \times 7^{10}$
Therefore, number of prime factors is equal to $4$ , i.e., ${2, 3, 5, 7}$

Hence, option D.