Question

Find each of these values.

a.(192 mod 41) mod 9

b.(323 mod 13)2 mod 11

c.(73 mod 23)2 mod 31

d.(212 mod 15)3 mod 22

Answer 1

$192=4\cdot41+28\iff192\equiv28\pmod{41}$
$28=3\cdot9+1\iff28\equiv1\pmod9$

$323=24\cdot13+11\iff323\equiv11\pmod{13}$
$11^2\equiv0\pmod{11}$

$73=3\cdot23+4\iff73\equiv4\pmod{23}$
$4^2\equiv16\pmod{31}$

$212=14\cdot15+2\iff212\equiv2\pmod{15}$
$2^3\equiv8\pmod{22}$

Answer 2

Remainders will be 1, 0, 16, and 8 for options a, b, c, and d respectively.

What is a remainder?

The Remainder is the extra part of a number that restricts the number to be divided completely.

a)192 = 4*41 +28

28 = 3*9 +1

So, answer will be 1.

b)323 = 24*13 + 11

11² = 121

121=11*11+0

So, answer will be zero.

c)73=3*23 + 4

4² =16

16 =0*31+16

So, answer will be 16.

d)212 = 14*15 + 2

2³ =8

8=0*22 +8

So, answer will be 8.

Hence, remainders will be 1, 0, 16, and 8 for options a, b, c, and d respectively.

To get more about remainders visit:

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