How do i write the sum of two numbers as the product of their gcf and another sum

1) Start by calculating the greatest common factor (GCF)

For example, take the sum 130 + 26.

Calculate the GFC:

i) prime decompostion:

130 = 2×5×13

26 = 2×13

ii) the GCF is the product of the common factors each raised to the lowest power: 2×13 = 26.

2) Use the GCF as factor of the two numbers: write the common factor, open parenthesis, and write inside the parenthesis the quotient of each number when divided by the GCF.

Following our example with the numbers 130 and 26:

26 ( 130÷26 + 26÷26) = 26 (5 + 1)

The result is 26 (5 + 1).

3) This calculation is named factoring and is the operation opposite to the use of the distributive property.

4) You can verify that 130 + 26 = 26 ( 5 + 1)

130 + 26 = 156

26 (5 + 1) = 26 × 6 = 156

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step-by-step explanation: