Number Theory Concepts

• These questions cover divisibility rules, remainders, prime numbers, factorization, LCM, GCD, perfect squares, and basic algebraic problem-solving.

Remainder Calculation

• When 193 is divided by 7, the remainder is 4.

Divisibility of 3456

• The number 3456 is divisible by 2, 3, and 6.

Finding a Number with Specific Remainders

• The number that leaves a remainder of 3 when divided by 4, 6, and 8 is 51.

Divisibility by 9

• The number 1236 is divisible by 9.

Divisibility of 8250

• The number 8250 is divisible by 2, 5, and 10.

Greatest Common Divisor

• The greatest number that divides 120, 180, and 240 without a remainder is 60.

Smallest 4-digit Number Divisible by 11

• The smallest 4-digit number divisible by 11 is 1001.

Divisibility by 9 Using Digit Sum

• Given a sum of digits of 15, the number 225 is divisible by 9

Least Common Multiple of 12 and 15

• The least common multiple (LCM) of 12 and 15 is 60.

Divisibility of 36

• 36 is divisible by 3, 6, and 9.

Identifying Prime Numbers

• 29 is a prime number.

Remainder Calculation for 425 ÷ 8

• When 425 is divided by 8, the remainder is 1.

Greatest Common Divisor of 24 and 36

• The greatest common divisor (GCD) of 24 and 36 is 12.

Exponent Calculation

• 2³ × 2⁴ equals 128.

Prime Factorization of 36

• The prime factorization of 36 is 2 × 2 × 3 × 3.

Solving for Product of Two Numbers

• If the sum of two numbers is 56 and their difference is 12, their product is 768.

Divisibility of 420

• The number 420 is divisible by 5, 6, and 12.

Counting Perfect Squares

• There are 9 perfect squares between 1 and 100

Identifying Perfect Cubes

• 27 is a perfect cube.

Number Divisible by 1 to 5

• The smallest number divisible by all numbers from 1 to 5 is 60.