Understanding Prime Factors and Divisibility

The video tutorial by Professor Von Schmohawk introduces the concept of factors, prime numbers, and composite numbers. It explains the Fundamental Theorem of Arithmetic, which states that any integer greater than one can be uniquely expressed as a product of prime numbers. The process of factoring is demonstrated through examples, including the numbers 420 and 849, showing how to break them down into their prime factors. The tutorial emphasizes the importance of factoring in mathematics, particularly in arithmetic operations involving fractions.

What is a factor of a number?

• A number that is equal to the given number

• A number that is less than the given number

• A number that is greater than the given number

• A number that divides another number without leaving a remainder

Which of the following is a prime number?

• 6

• 7

• 9

• 4

What is a composite number?

• A number that cannot be factored

• A number with only one factor

• A number with exactly two factors

• A number with more than two factors

What does the Fundamental Theorem of Arithmetic state?

• Every integer is a composite number

• Every integer can be divided by two

• Every integer greater than one can be written as a unique product of prime numbers

• Every integer is a prime number

What is the first step in factoring a number?

• Divide the number by itself

• Check if the number is even

• Multiply the number by two

• Test each prime number to see if it divides evenly into the number

Which of the following is a prime factor of 420?

• 6

• 8

• 4

• 5

What is the sum of the digits of 105?

• 7

• 6

• 5

• 8

Which prime number is used to test if 35 is composite?

• 5

• 3

• 2

• 7

What is the result of dividing 849 by 3?

• 285

• 287

• 281

• 283

Which prime number is not a factor of 283?

• 5

• 11

• 7

• 3