Final answer:
The GCF of 49 and 14 is 7. By dividing each term by 7, the expression 49t+14 is factored to 7(7t + 2).
Step-by-step explanation:
To factor the expression 49t + 14 by dividing by the Greatest Common Factor (GCF), we first need to determine what the largest number is that divides both 49 and 14 evenly. The GCF of 49 and 14 is 7. So, we divide both terms in the expression by 7 to factor it.
Here is the step-by-step factoring:
- First, we write down the numbers 49 and 14.
- Next, we list the factors of each number:
- Factors of 49: 1, 7, 49
- Factors of 14: 1, 2, 7, 14
- We then identify the highest common factor, which is 7.
- Now, we divide both terms of the expression by 7.
- The expression becomes 7(7t + 2).
By dividing each term by the GCF, we successfully factored the expression.