Divisibility Rules and Prime Factorization

The video tutorial explains how to perform prime factorization of a large number using short division. It emphasizes the importance of knowing multiplication tables and divisibility rules for smaller primes. The tutorial demonstrates the process with the number 76,230, dividing it by 2, 5, 3, and 7, and finally using 11 to complete the factorization. The result is expressed using exponential notation for repeated factors. The method is presented as a fast and efficient way to factorize large numbers.

What is the primary method discussed for quickly performing prime factorization on large numbers?

• Using a calculator

• Short division

• Guess and check

• Long division

Which rule of divisibility is used to determine if a number is divisible by 2?

• The sum of the digits is divisible by 3

• The number is even

• The number is a multiple of 10

• The number ends in 0 or 5

How do you determine if a number is divisible by 5?

• The sum of the digits is divisible by 3

• The number ends in 0 or 5

• The number is even

• The number is a multiple of 10

What is the rule for checking divisibility by 3?

• The number is a multiple of 10

• The sum of the digits is divisible by 3

• The number ends in 0 or 5

• The number is even

If the sum of the digits of a number is 18, is the number divisible by 3?

• No

• Yes

• Only if it ends in 5

• Only if it ends in 0

What is the divisibility rule for 7?

• Double the last digit and subtract from the rest

• The number ends in 0 or 5

• The sum of the digits is divisible by 3

• The number is a multiple of 10

How can you verify if a number is divisible by 7 using the times table?

• Add the digits and check if the sum is 7

• Check if the number ends in 7

• Use the 7 times table to see if it fits

• Double the last digit and subtract from the rest

What is the prime factorization of 121?

• 14 * 8

• 11 * 11

• 12 * 10

• 13 * 9

How do you express repeated prime factors using exponential notation?

• By using a power to indicate repetition

• By multiplying the factors

• By adding the factors

• By listing the factors multiple times

What is the final step in prime factorization using short division?

• Check divisibility by 9

• Gather all prime factors and use exponential notation

• Multiply all factors together

• Divide by 10