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Number of factors of 6!
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08 Apr 2025, 10:20
08 Apr 2025, 10:20
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Quantity A |
Quantity B |
Number of factors of 6! |
Number of factors of 735 |
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Re: Number of factors of 6!
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12 Apr 2025, 04:15
12 Apr 2025, 04:15
Expert Reply
Column A: $\(6!=2 \times 3 \times 4 \times 5 \times 6=2^4 \times 3^2 \times 5\)$.
Therefore, the total number of factors of $\(6!=(4+1)(2+1)(1+1)=5 \times 3 \times 2=30\)$. Column B: $\(735=5 \times 147=5 \times 7 \times 21=5 \times 7^2 \times 3\)$.
Therefore, the total number of factors of $7\(35=(2+1)(1+1)(1+1)=3 \times 2 \times 2=12\)$. Hence, Column $\(\mathrm{A}>\)$ Column B. Thus, the correct answer is $\(A\)$.
Therefore, the total number of factors of $\(6!=(4+1)(2+1)(1+1)=5 \times 3 \times 2=30\)$. Column B: $\(735=5 \times 147=5 \times 7 \times 21=5 \times 7^2 \times 3\)$.
Therefore, the total number of factors of $7\(35=(2+1)(1+1)(1+1)=3 \times 2 \times 2=12\)$. Hence, Column $\(\mathrm{A}>\)$ Column B. Thus, the correct answer is $\(A\)$.
gmatclubot
Re: Number of factors of 6! [#permalink]
12 Apr 2025, 04:15
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