Question

put the steps to find the greatest common factor (gcf) in order, with the first step at the top and last step at the bottom, assume you are finding the gcf of two numbers (1 point)

• actually multiply the common prime factors together, the product is your gcf
• break up the numbers into prime factors, using a factor tree or list.
• list the common prime factors in an expression being multiplied together.
• match up prime factors that are on both factor trees/lists, these are your common prime factors.

show how to find the greatest common factor of 90, and 252. show all your work, show every step (3 points)

Explanation:

Step1: Prime Factorization

Break down 90 and 252 into prime factors.
For 90: \( 90 = 2 \times 45 = 2 \times 3 \times 15 = 2 \times 3 \times 3 \times 5 \)
For 252: \( 252 = 2 \times 126 = 2 \times 2 \times 63 = 2 \times 2 \times 3 \times 21 = 2 \times 2 \times 3 \times 3 \times 7 \)

Step2: Identify Common Prime Factors

Find the prime factors common to both.
Common prime factors: \( 2, 3, 3 \) (since 2 appears at least once, 3 appears at least twice in both factorizations).

Step3: List Common Prime Factors

Write the common prime factors as a product: \( 2 \times 3 \times 3 \)

Step4: Multiply Common Prime Factors

Calculate the product of the common prime factors: \( 2 \times 3 \times 3 = 18 \)

Answer:

The GCF of 90 and 252 is 18. The steps are: 1) Prime factorize 90 (\(2 \times 3^2 \times 5\)) and 252 (\(2^2 \times 3^2 \times 7\)); 2) Identify common primes (\(2, 3, 3\)); 3) Multiply them (\(2 \times 3 \times 3 = 18\)).