Questions: Find the greatest common factor for the list of monomials. x^4 y^5 z^5, y^3 z^5, x y^3 z^3 The GCF is

Solution Steps

• The first monomial \( x^{4} y^{5} z^{5} \) has:
  • \( x \) with exponent 4,
  • \( y \) with exponent 5,
  • \( z \) with exponent 5.
• The second monomial \( y^{3} z^{5} \) has:
  • \( y \) with exponent 3,
  • \( z \) with exponent 5.
• The third monomial \( x y^{3} z^{3} \) has:
  • \( x \) with exponent 1,
  • \( y \) with exponent 3,
  • \( z \) with exponent 3.

• For \( x \):
  • The exponents are 4, 0 (since \( x \) is not present in the second monomial), and 1.
  • The smallest exponent is 0.
• For \( y \):
  • The exponents are 5, 3, and 3.
  • The smallest exponent is 3.
• For \( z \):
  • The exponents are 5, 5, and 3.
  • The smallest exponent is 3.

• The GCF is \( x^{0} y^{3} z^{3} \), which simplifies to \( y^{3} z^{3} \).

Final Answer