1. Greatest Common Factor
Factors
and
Greatest Common Factor

2. What numbers can be multiplied together to get 24?
The number 24 is called the product because it is the result of multiplying two or more numbers together.
1 x 24
2 x 12
3 x 8
The numbers 1, 2, 3, 4, 6, 8, 12, and 24 are called factors. These are the numbers being multiplied together.
4 x 6
What are the factors of seven?
1 x 7
Composite numbers – numbers which have two or more factors like the number 24.
Prime numbers – numbers having exactly two factors: one and itself. Seven is a prime number.

3. Prime Factorization Factor 56 using only prime factors.
To do this, we can make a factor tree as follows. 56
28 is composite so we can factor it further.
2 is prime. 2 × 28
14 is composite, so we can factor it further.
2 is prime. 2 × 14
2 is prime. 2 ×
7 is prime. 7
The prime factorization of 56 is 2 × 2 ×2 × 7 or 23 × 7.

4. Prime Factorization or
We can make a factor tree using different starting factors. 56
14 is composite so we can factor it further.
4 is composite so we can factor it further. 4 × 14 × 2 × 2 2 7
2 is prime.
7 is prime.
The prime factorization of 56 is 2 × 2 × 2 × 7 or 23 × 7.
The prime factorization of every number is unique. No matter what factors you choose, the prime factorization will still be the same for that number.

5. _______ _____ _____
Find the prime factorization of the following two numbers. 60
105 2 × 30 5 × 21 2 × 15 3 × 7
60 = 2 × 2 × 3 × 5. 3 × 5
105 = 3 × 5 × 7
What factors do these two numbers have in common?
3 and 5
The greatest common factor of 60 and 105 is 3 × 5 or 15.

6. You Try It Find the greatest common factor (GCF) of the monomials.
, 85
Determine whether each number is prime or composite. If the number is composite, find its prime factorization.
4. To find the area of a rectangle, you multiply length times width. If a rectangle has an area of 124 square centimetres, what are its possible dimensions?

7. Problems 2 &3 2. 145 is composite. 145 = 5 × 29
is a prime number.

8. Problem 4 The area of a rectangle is the product of two factors.
The factors of 124 are:
1 x 24
2 x 62
4 x 31
Therefore, the possible dimensions of the rectangle are
1 cm x 124 cm
2 cm. x 62 cm
4 cm x 31 cm