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