The expression 25 + 75 can be rewritten as 25 * (1 + 3) by factoring out their greatest common factor (GCF), which is 25. This simplifies the expression while preserving its original value.
Rewriting 25 + 75 using GCF and multiplication:
Here's how we can rewrite 25 + 75 using their greatest common factor (GCF) and multiplication:
1: Find the GCF of 25 and 75.
The GCF is the largest number that is a factor of both 25 and 75. We can find it by prime factorization:
25 = 5 * 5
75 = 3 * 5 * 5
The only common prime factor is 5 (appearing twice in 75), so the GCF is 5 * 5 = 25.
2: Divide each number by the GCF.
Now, we divide each number in the sum by the GCF:
25 / 25 = 1
75 / 25 = 3
3: Rewrite the expression using multiplication.
Finally, we rewrite the original sum using the GCF and the quotients from step 2:
25 + 75 = (25 * 1) + (25 * 3)
Therefore, the rewritten expression using GCF and multiplication is:
25 * (1 + 3)
This expression is equivalent to the original sum 100 but highlights the common factor of 25 and simplifies the addition.