Multiples, Factors, Primes & Composite Numbers Greatest Common Factors

Definition Product Product – An answer to a multiplication problem. 7 x 8 = 56 Product

Definition Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors

Definition Factor – a number that divides evenly into another. 56 ÷ 8 = 7 Factor

What are the factors? 6 x 7 = 42 6 & 7 7 x 9 = 63 7 & 9 8 x 6 = 48 8 & 6 4 & 9 4 x 9 = 36

What are the factors? 42 ÷ 7 = 6 7 63 ÷ 9 = 7 9 48 ÷ 6 = 8 6 9 36 ÷ 9 = 4

FACTORS OF SOME NUMBERS 8 = 1x8, 2x4 Factors of 8: 1, 2, 4, 8 16 = 1x16, 2x8, 4x4 Factors of 16 : 1, 2, 4, 8, 16 25 = 1 x25, 5x5, Factors of 26: 1, 5, 25

4 × 5 = 20 4 and 5 are factors of 20. We can also say that 20 is multiple of 4 and 5. In 2 × 12 = 24, 2 and 12 are factors of 24. 24 is the multiple of 2 and 12. So, a number is a multiple of its factors.

4 × 5 = 20 Factors Multiple

The number of multiples of a given number is infinite.

POINTS TO REMEMBER 1 is a factor of every number. Every factor of a number is an exact divisor of that number. Every factor is less than or equal to the given number. Number of factors of a given number are finite.

FACTOR OR MULTIPLE? For each of numbers in the statements, select either multiple [M] or factor [F] 34 × 5 = 170 [F] [M] [F] [M] [F] [M] 25 × 4 = 100 90 × 10 = 900 45 × 6 = 270 7 × 30 = 210

State whether the following statements are TRUE or FALSE 1. 1 is a factor of every number. F T 2. The largest factor of any number is the number itself. F T 3. Number of factors of a given number is infinite. F T 4.The number of multiples of 5 is 10. F T 5.The factors of 65 are 1, 5 and 13 only. F T

CORRECT

WRONG

7 Definition 7 is prime because the only numbers Prime Number – a number that has only two factors, 1 and itself. 7 7 is prime because the only numbers that will divide into it evenly are 1 and 7.

Examples of Prime Numbers 2, 3, 5, 7, 11, 13, 17, 19 Special Note: One is not a prime number.

8 Definition The factors of 8 are 1, 2, 4, 8 Composite number – a number that has more than two factors. 8 The factors of 8 are 1, 2, 4, 8

Examples of Composite Numbers 4, 6, 8, 9, 10, 12, 14, 15 Special Note: Every whole number from 2 on is either composite or prime.

Our Lonely 1 One is not a prime nor a composite number. It is not prime because it does not have exactly two different factors. It is not composite because it does not have more than 2 factors. Special Note: One is not a prime nor a composite number.

Finding The Greatest Common Factor

Greatest Common Factor The greatest common factor is the largest common factor of two numbers. Factors are all of the numbers that divide into a given number equally. The greatest common factor can be found by comparing all the factors of two numbers or by finding the prime factorization of two numbers

Finding Factors Finding the factors of a number can be done by sequentially dividing numbers into the product. When the factors begin to repeat you have found all factors.

We are now back to 6. We have found all factors of 18. Finding Factors Find the factors of 18 1 goes into 18, 18 times. 2 goes into 18, 9 times. 3 goes into 18, 6times. 4 does not divide 18 evenly. 5 does not divide 18 evenly. We are now back to 6. We have found all factors of 18. 1, 2, 3, 6 and 18

Finding The GCF Using Factors Determine the greatest common factor of two numbers by finding all the factors for the two numbers then comparing them. The largest common factor of the two numbers is their greatest common factor.

The greatest common factor is of 36 and 24 is 12 Using Factors Find the GCF of 36 and 24 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36 Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24 The greatest common factor is of 36 and 24 is 12

The greatest common factor of 48, 24, and 36 is 12. EXAMPLE Find the factors of 48, 24 & 36 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 1, 2, 3, 4, 6, 12 The common factors are 1, 2, 3, 4, 6, and 12. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 3, 4, 6, 12 The GCF is 12. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 1, 2, 3, 4, 6, 12 ANSWER The greatest common factor of 48, 24, and 36 is 12.

The greatest common factor of 15 and 100 is 5 Using Factors Again Find the GCF of 15 and 100 Factors of 15: 1, 3, 5 and 15 Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100 The greatest common factor of 15 and 100 is 5