Using the greatest common factor for the terms how can you write 45+75
15 (3 + 5)
15 (3 + 5)
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To write 45+75 using the greatest common factor (GCF) of the terms, we need to first find the GCF of 45 and 75. The greatest common factor is the largest number that divides both 45 and 75 evenly.
To find the GCF, we can start by listing the factors of each number:
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 75: 1, 3, 5, 15, 25, 75
Looking at the lists, we can see that the common factors of 45 and 75 are 1, 3, 5, and 15. Among these, the largest common factor is 15.
Now that we have the GCF of 45 and 75, we can rewrite the expression as a product of the GCF and the term inside parentheses:
45 + 75 = 15 * (45/15 + 75/15)
Simplifying the terms inside the parentheses:
45/15 = 3
75/15 = 5
Substituting the values back into the expression:
15 * (3 + 5)
Calculating the sum inside the parentheses:
15 * 8 = 120
Therefore, using the greatest common factor, 45 + 75 simplifies to 120.