9515 1404 393
Answer:
2×5×11 = 110
Step-by-step explanation:
The factors are separated by the × (multiplication) sign. Common factors are numbers that are factors of both products.
It can be useful to list the factors in order of size, for easier comparison.
1st product:
2 × 3² × 5² × 11 × 17
2nd product:
2 × 5 × 7 × 11² × 13²
Ignoring exponents (for the moment), the numbers that appear in both products are 2, 5, 11. (I've highlighted them so you can see them more easily.)
Now, we consider the exponents. We want to determine the lowest exponent of each of these factors.
2 has the same exponent in both products: 1
5 has exponents of 2 and 1. The least of these is 1.
11 has exponents of 1 and 2. The least of these is 1.
So, the greatest common factor (GCF) is ...
2¹ × 5¹ × 11¹ = 2×5×11 = 110 . . . . greatest common factor
(Comment on answer format: the given numbers are shown as a product of factors. It is not clear whether the desired answer format should match, or should have the value multiplied out. We have shown both ways.)
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Check
If we factor out the "greatest common factor," the given products can be written as ...
(2×5×11) × (3² × 5 × 17)
(2×5×11) × (7 × 11 × 13²)
You will notice that the right factors of each of these products have nothing in common. So, we have found the greatest common factor.
