Choose the correct greatest common factor of 75, 195, and 325.
75 = 3 * 5 * 5
195 = 3 * 13 * 5
325 = 5 * 5 * 13
well, right off you see that only a single 5 is common to all three.
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1.7
To find the greatest common factor (GCF) of 75, 195, and 325, we need to determine the highest number that divides evenly into all three numbers.
One way to find the GCF is by factoring the numbers into their prime factors and then identifying the common factors:
1. Start by factoring each number into its prime factors:
- 75 = 3 * 5 * 5
- 195 = 3 * 5 * 13
- 325 = 5 * 5 * 13
2. Now, identify the common prime factors among the three numbers:
- 3 and 5 are common factors of 75 and 195.
- 5 and 13 are common factors of 195 and 325.
3. The GCF is the product of the common prime factors with the smallest exponent:
- The common factors of 75 and 195 are 3 and 5, and they both have an exponent of 1 (no repeated factors), so we take their product: GCF = 3 * 5 = 15.
- The common factors of 195 and 325 are 5 and 13, and they both have an exponent of 1, so we take their product: GCF = 5 * 13 = 65.
Since we are looking for the greatest common factor, the correct answer is the larger value, which is 65.
Therefore, the correct greatest common factor of 75, 195, and 325 is 65.