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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

47

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

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.

Suggest Corrections

Similar questions

Q. The number of prime factors of

{(3 \times 5)}^{12} {(2 \times 7)}^{10} {(10)}^{25}

Q. The number of prime factors in the expression

(6)^{4} \times (8)^{6} \times (10)^{8} \times (12)^{10}

Q. The number of prime factors in

{(\frac{1}{6})}^{12} \times (8)^{25} \times {(\frac{3}{4})}^{15}

Q. Total number of factors of a number is 24 and the sum of its 3 prime factors out of four, is 25. The product of all 4 prime factors of this number is 1365. Then such a greatest possible number can be

Question 28
The number of distinct prime factors of the smallest 5-digit number is

(A) 2
(B) 4
(C) 6
(D) 8

Join BYJU'S Learning Program

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.