What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100?
- A0Correct
- B1
- C2
- D4
Explanation
To find the remainder when the product is divided by 100, we need to check if the product is divisible by 100. 100 can be factored as 4 x 25.
Let's examine the factors of the numbers in the product:
- 85 contains a factor of 5 (85 = 5 x 17).
- 95 contains another factor of 5 (95 = 5 x 19). So, from 85 and 95, we have 5 x 5 = 25 as a factor in the product.
- 96 contains a factor of 4 (96 = 4 x 24).
Since the product contains 25 (from 85 and 95) and 4 (from 96) as factors, it means the entire product is divisible by 25 x 4 = 100.
When a number is completely divisible by another number, the remainder is 0.
Therefore, the remainder when 85 x 87 x 89 x 91 x 95 x 96 is divided by 100 is 0.
The final answer is A) 0.
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