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How many factors of 6! are greater than 100?

This topic has 2 expert replies and 0 member replies

How many factors of 6! are greater than 100?

Post Sun Nov 05, 2017 4:19 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    How many factors of 6! are greater than 100?

    (A) 4
    (B) 5
    (C) 7
    (D) 10
    (E) 12

    I'm confused how to set up the formulas here. Can any experts help?

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    Post Sun Nov 05, 2017 5:37 am
    ardz24 wrote:
    How many factors of 6! are greater than 100?

    (A) 4
    (B) 5
    (C) 7
    (D) 10
    (E) 12
    Start with the GREATEST FACTOR and work down to the smallest factor greater than 100.

    6! = 6*5*4*3*2.

    Case 1: Combine 5 of the values in blue to yield a product greater than 100
    6*5*4*3*2
    Total options = 1.

    Case 2: Combine 4 of the values in blue to yield a product greater than 100
    6*5*4*3
    6*5*4*2
    6*5*3*2
    6*4*3*2
    5*4*3*2
    Total options = 5.

    Case 3: Combined 3 of the values in blue to yield a product greater than 100
    6*5*4
    Discard this option, since 6*5*4 is the same as 5*4*3*2, counted above.

    Total options = Case 1 + Case 2 = 1+5 = 6.

    The OA is not among the answer choices.
    What is the source of this problem?

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    Thanked by: ardz24
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    Post Sun Nov 05, 2017 12:29 pm
    Hi ardz24,

    We're asked for the number of factors of 6! that are greater than 100. Since 6! is a relatively easy number to deal with, we can 'brute force' the solution by listing out the factors that are greater than 100:
    (1)(720)
    (2)(360)
    (3)(240)
    (4)(180)
    (5)(144)
    (6)(120)
    (8)(90)

    At this point, we can stop working. Each of the first 6 pairs has a factor greater than 100, but as the first number in each pair increases, the second number will decrease (thus, there's no reason to look at 'pairs' above 8 and 90).

    Final Answer: 6 factors

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    Thanked by: ardz24

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