How to Use the GCF to Factor 35 + 63

Use the GCF to Factor 35 + 63

Factoring expressions is a crucial skill in algebra that simplifies calculations and reveals useful properties of numbers. Here, we’ll use the greatest common factor (GCF) to factor the expression 35 + 63 step by step.

Step 1: Find the GCF of 35 and 63

The greatest common factor (GCF) is the largest number that divides evenly into both 35 and 63. To find it, follow these steps:

1. Prime Factorization of 35:35 = 5×7
2. Prime Factorization of 63:63 = 3²×7
3. Identify the common factors. Both 35 and 63 share a factor of 7.

Thus, the GCF of 35 and 63 is 7.

Step 2: Factor Out the GCF

Rewrite each term of the expression as a product of the GCF and another factor:

35+63 = 7x (5+9)

Now, use the distributive property to factor out the GCF:

35+63 = 7(5+9)

Step 3: Simplify Inside the Parentheses

Simplify the expression inside the parentheses:

7(5+9) = 7(14)

Final Answer

The factored form of 35 + 63 is:

7(14)

Why Is Factoring Useful?

Factoring expressions using the GCF is helpful for:

• Simplifying expressions
• Solving equations
• Revealing common patterns in numbers

By understanding how to use the GCF, you can simplify your calculations and gain a deeper appreciation for the structure of numbers!