Free Practice Question
PS · Problem Solving
655-705
Divisibility/Multiples/Factors
What is the highest power of 5 that will divide the product of the first 40 multiples of 5?
Answer Choices
Correct answer marked belowA
39
B
40
C
45
49
Correct
E
59
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Explanation
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Official Explanation
Official
To find the highest power of 5 that divides the product of the first 40 multiples of 5, we consider: 5*1, 5*2, 5*3, ..., 5*40. The product can be expressed as: 5*1 x 5*2 x 5*3 x ... x 5*40 = 5^{40} * (1 * 2 * 3 * ... * 40) = 5^{40} *…
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What it tests
Your understanding of divisibility rules, least common multiples, and greatest common factors.
Common trap
Forgetting that 1 is not prime and that every integer divides 0.
Details
Difficulty
655-705
Type
PS
Category