What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100?

Question

Accepted Answer

To find the remainder when 85 x 87 x 89 x 91 x 95 x 96 is divided by 100, we need to check if 100 is a factor of the product.

1.  Identify the factors of 100: 100 = 4 x 25.
2.  Look for factors of 4 and 25 (or factors of 5 and 5 and 4) within the numbers in the product:
    *   85 is divisible by 5 (85 = 5 x 17).
    *   95 is divisible by 5 (95 = 5 x 19).
    *   96 is divisible by 4 (96 = 4 x 24).
3.  Combine these factors: The product contains (5 from 85) x (5 from 95) x (4 from 96).
    This gives 5 x 5 x 4 = 25 x 4 = 100.
4.  Since 100 is a factor of the product (85 x 87 x 89 x 91 x 95 x 96 = (100 x 17 x 19 x 24 x 87 x 89 x 91)), the entire product is a multiple of 100.
5.  Any multiple of 100, when divided by 100, leaves a remainder of 0.

Therefore, the remainder is 0.

The final answer is A) 0.

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0

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What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100?

Explanation

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