What is the remainder when the product of the first 10 prime numbers i

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.



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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