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All but one term are divisible by 14. So the remainder of that product (775*778) divided by 14 is the remainder of the product of their remainders (ab) divided by 14 only. Here, the remainder of 775/14 is 5 and the remainder of 778/14 is 8. Their product (ab) = 5*8 = 40. The remainder of 40/14 is 12. So the remainder of 775*778/14 is the same, 12.

Again all but one term are divisible by 14. In other words, it's the remainder of that product of the numbers/14 is the remainder of abc/14, only.

General rule: The remainder of the product of three large numbers divided by \(x\) is the remainder of the product of their remainders divided by \(x\).

Answer to the OP: The following are easy to determine: The remainder of 775/14 is 5 The remainder of 778/14 is 8 The remainder of 781/14 is 11

Finally, the remainder of (775 * 778 * 781)/14 is simply the remainder of the product of their remainders divided by 14:

Re: If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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11 Jul 2017, 21:01

Bunuel wrote:

If N = 775 × 778 × 781, what is the remainder when N is divided by 14?

A. 6 B. 7 C. 8 D. 9 E. 10

if you divide each number by 14 then the remainder for the numbers are 5,8 & 11. i multiplied all the remainders and divided it by 14 (5x8x11/14). the remainder was 6.

If N = 775 × 778 × 781, what is the remainder when N is divided by 14?
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14 Jan 2019, 17:02

Top Contributor

Bunuel wrote:

If N = 775 × 778 × 781, what is the remainder when N is divided by 14?

A. 6 B. 7 C. 8 D. 9 E. 10

First recognize that 770 is the biggest multiple of 14 that is less than 775, 778 and 781 770 = (14)(55), but let's just say that 770 = 14k (where k = 55)

This means 775 = 14k + 5, 778 = 14k + 8 and 781 = 14k + 11