MODULAR DIVISION QUIZ

For Modular Arithmetic what value is the most important?

• The Modulo

• The Given Number

• The Remainder

• The Divisor

Answer explanation

In modular arithmetic, the remainder is crucial as it represents the result of the division of one number by another, indicating how much is left over. Thus, the remainder is the most important value.

What is 7 mod 3?

• 1 mod 3

• 2 mod 3

• 3 mod 3

• 0 mod 3

Answer explanation

To find 7 mod 3, divide 7 by 3, which gives a quotient of 2 and a remainder of 1. Therefore, 7 mod 3 equals 1. The correct answer is 1 mod 3.

What is 57 mod 7?

• 0 mod 7

• 1 mod 7

• 7 mod 7

• -1 mod 7

Answer explanation

To find 57 mod 7, divide 57 by 7, which gives a quotient of 8 and a remainder of 1. Thus, 57 mod 7 equals 1, making '1 mod 7' the correct answer.

What is 99 mod 100?

• 99 mod 100

• 100 mod 99

• 1 mod 100

• 100 mod 1

Answer explanation

99 mod 100 means the remainder when 99 is divided by 100. Since 99 is less than 100, the remainder is 99 itself. Therefore, the correct answer is 99 mod 100.

What is 14 mod 8 - 15 mod 8 congruent to?

• 7 mod 8

• 1 mod 8

• 0 mod 8

• 6 mod 8

Answer explanation

14 mod 8 = 6 and 15 mod 8 = 7. Therefore, 14 mod 8 - 15 mod 8 = 6 - 7 = -1, which is congruent to 7 mod 8. Thus, the correct answer is 7 mod 8.

What is 5 mod 4?

• 1

• 2

• 3

• 4

Answer explanation

To find 5 mod 4, divide 5 by 4, which gives a quotient of 1 and a remainder of 1. Therefore, 5 mod 4 equals 1, making the correct answer 1.

What is 3 mod 12?

• 1

• 2

• 3

• 4

Answer explanation

To find 3 mod 12, we calculate the remainder of 3 divided by 12. Since 3 is less than 12, the remainder is simply 3. Therefore, 3 mod 12 equals 3.

What is 100 mod 100?

• 50

• 1

• 0

• 99

Answer explanation

To find 100 mod 100, we calculate the remainder of 100 divided by 100. Since 100 is exactly divisible by 100, the remainder is 0. Therefore, 100 mod 100 equals 0.

What is 18 mod 4?

• 0

• 1

• 2

• 4

Answer explanation

To find 18 mod 4, divide 18 by 4, which gives a quotient of 4 and a remainder of 2. Thus, 18 mod 4 equals 2, making the correct answer 2.

What is 12 mod 12?

• 1

• 0

• 2

• 12

Answer explanation

12 mod 12 calculates the remainder when 12 is divided by 12. Since 12 divides evenly into 12 with no remainder, the result is 0. Therefore, the correct answer is 0.