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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the remainder when the product of the first 10 prime tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## What is the remainder when the product of the first 10 prime ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] What is the remainder when the product of the first 10 prime numbers is divided by 4? A. 0 B. 1 C. 2 D. 3 E. not defined _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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What is the remainder when 30 is divided by 4?

One approach:
1. Break the dividend 30 into factors: 30 = 5*6
2. Divide the divisor 4 into each factor: 5/4 = 1 R1, 6/4 = 1 R2
3. Multiple the resulting remainders: 1*2 = 2

Step 3 indicates that 30 divided by 4 will yield a remainder of 2.
This approach can be applied to any problem that asks for the remainder when a large integer or product is divided by a divisor.
Repeat the 3 steps until the value yielded by Step 3 is less than the divisor.

Max@Math Revolution wrote:
[GMAT math practice question]

What is the remainder when the product of the first 10 prime numbers is divided by 4?

A. 0
B. 1
C. 2
D. 3
E. not defined
Product of the first 10 prime numbers = 2*3*5*7*11*13*17*19*23*29

Dividing 4 into each of the prime factors above yields the following remainders:
2*3*1*3*3*1*1*3*3*1 = 6*9*9

Dividing 4 into each of the factors in red yields the following remainders:
2*1*1 = 2

Since the result in blue is less than the divisor of 4, the desired remainder is 2.

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2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first 10 prime numbers.
Of these, only 2 is an even integer. Their product is an even number, but it is not divisible by 4.
Thus, the product has remainder 2 when it is divided by 4.

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