Question

Compute the value of the following expressions: 323 mod 5 323 div 5 −323 mod 5 −323 div 5 327 mod 3 (64 · (−67) + 201) mod 7 (〖38〗^12) mod 6 (〖38〗^12) mod 3

Answer 1

323 mod 5 = 3

−323 mod 5 = -3

327 mod 3 = 0

(64 * (-67) + 201) mod 7 = 6

(38^12) mod 6 = 4

(38^12) mod 3 = 1

Explanation:

The modulo operation looks for remainders from the quotients. In order to find them, divide the whole number by the mod number. Then take just the decimal after the whole answer and multiply it by the mod number.

323 mod 5

323/5 = 64.6

.6 * 5 = 3

−323 mod 5

323/5 = -64.6

-.6 * 5 = -3

327 mod 3

327/5 = 109

0 * 3 = 0

(64 * (-67) + 201) mod 7

64 * -67 = -4288 + 201 = 4087

4087/7 = 583.85714

.85714 * 7 = 6

(38^12) mod 6

38^12 = 9.07x10^18

9.07x10^18/6 = 1510956318082499242.6666667

.666667 * 6 = 4

(38^12) mod 3

38^12 = 9.07x10^18

9.07x10^18/3 = 3021912636164998485.333333

.3333333 * 3 = 1

Answer 2

323 mod 5 = 3

−323 mod 5 = -3

327 mod 3 = 0

(64 * (-67) + 201) mod 7 = 6

(38^12) mod 6 = 4

(38^12) mod 3 = 1

Explanation:

The modulo operation looks for remainders from the quotients. In order to find them, divide the whole number by the mod number. Then take just the decimal after the whole answer and multiply it by the mod number.

323 mod 5

323/5 = 64.6

.6 * 5 = 3

−323 mod 5

323/5 = -64.6

-.6 * 5 = -3

327 mod 3

327/5 = 109

0 * 3 = 0

(64 * (-67) + 201) mod 7

64 * -67 = -4288 + 201 = 4087

4087/7 = 583.85714

.85714 * 7 = 6

(38^12) mod 6

38^12 = 9.07x10^18

9.07x10^18/6 = 1510956318082499242.6666667

.666667 * 6 = 4

(38^12) mod 3

38^12 = 9.07x10^18

9.07x10^18/3 = 3021912636164998485.333333

.3333333 * 3 = 1