Understanding Short Division and Modular Congruence

What is the main advantage of short division over long division?

• It is easier to learn.

• It uses a calculator.

• It is more accurate.

• It requires less writing and is faster.

In short division, what do you primarily write down?

• The quotient and divisor.

• Only the remainders.

• The dividend and divisor.

• The entire division process.

How can you determine if a number is divisible by another using short division?

• By checking if the dividend is a multiple of the divisor.

• By checking if the remainder is zero.

• By checking if the quotient is a whole number.

• By checking if the divisor is larger than the dividend.

What is modular congruence primarily used for?

• Solving algebraic equations.

• Understanding number theory and cryptography.

• Determining divisibility.

• Calculating square roots.

What does it mean if a number is congruent to 0 mod another number?

• The number is a multiple of 10.

• The number is less than the modulus.

• The number is divisible by the modulus.

• The number is a prime number.

What is the remainder when 582 is divided by 7?

• 0

• 3

• 1

• 2

How can you express 1452 in terms of modular congruence with modulus 11?

• 1452 is congruent to 1 mod 11

• 1452 is congruent to 2 mod 11

• 1452 is congruent to 0 mod 11

• 1452 is congruent to 3 mod 11

What is the remainder when 2^491 is divided by 11?

• 0

• 1

• 3

• 2

Which mathematical concept is used to solve the problem of finding the remainder of 2^491 divided by 11?

• Long division

• Short division

• Modular congruence

• Prime factorization

What is the first step in solving a large exponent problem using modular congruence?

• Guessing the answer.

• Using a calculator.

• Simplifying the exponent using rules.

• Performing long division.