QuestionFind the GCF of 48 and 30, then express as .
Studdy Solution
STEP 1
Assumptions1. We are given two numbers,48 and30.
. We need to find the Greatest Common Factor (GCF) of these two numbers.
3. We need to express the sum of these two numbers as the product of their GCF and another sum.
STEP 2
First, we need to find the GCF of48 and30. The GCF is the largest number that divides both numbers without leaving a remainder.
We can find the GCF by listing the factors of each number and finding the largest number that appears in both lists.
STEP 3
The factors of48 are1,2,3,,6,8,12,16,24,48.
The factors of30 are1,2,3,5,6,10,15,30.
The common factors are1,2,3,6.
So, the GCF of48 and30 is6.
STEP 4
Now, we need to express the sum of48 and30 as the product of their GCF (6) and another sum.
Let's denote the sum of48 and30 as. So, =48 +30.
STEP 5
Calculate the sum.
STEP 6
Now, we need to express78 as the product of6 and another sum.
We can write78 as6 times13, because6 times13 equals78.
STEP 7
So, we can write the sum of48 and30 as the product of their GCF and another sum as followsThis completes the problem. The sum of48 and30 can be expressed as the product of their GCF (6) and another sum (13).
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