# What is the greatest common factor of 60x^{4}y^{7}, 45x^{5}y^{5}, and 75x^{3}y?

**Solution:**

The algebraic expressions given are

60x^{4}y^{7}, 45x^{5}y^{5}, and 75x^{3}y

By using the prime factorization method and laws of exponents

60x^{4}y^{7} = **3 × 5** × 4 × **x ^{3}** × × x × y

^{6}×

**y**

45x^{5}y^{5} = **3 × 5** × **x**^{3 }× x^{2} × y^{2} × y^{2}× **y**

75x^{3}y = **3 × 5** × 5 × **x ^{3} × y**

15 is the common coefficient and the common factor is x^{3}y.

Therefore, the greatest common factor is 15x^{3}y.

## What is the greatest common factor of 60x^{4}y^{7}, 45x^{5}y^{5}, and 75x^{3}y?

**Summary:**

The greatest common factor of 60x^{4}y^{7}, 45x^{5}y^{5}, and 75x^{3}y is 15x^{3}y.

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