Question 1: Find the greatest common factor (GCF/HCF) of the following polynomial:
2x^{2} and 12x^{2}
Answer 1: The numerical coefficients of the given monomials are 2 and 12. So, the greatest common factor of 2 and 12 is 2.
The common literal appearing in the given monomials is x.
The smallest power of x in the two monomials is 2.
The monomial of the common literals with the smallest powers is x^{2}.
Hence, the greatest common factor is 2x^{2}.
Question 2: Find the greatest common factor (GCF/HCF) of the following polynomial:
6x^{3}y and 18x^{2}y^{3}
Answer 2: The numerical coefficients of the given monomials are 6 and 18. The greatest common factor of 6 and 18 is 6.
The common literals appearing in the two monomials are x and y.
The smallest power of x in the two monomials is 2.
The smallest power of y in the two monomials is 1.
The monomial of the common literals with the smallest powers is x^{2}y.
Hence, the greatest common factor is 6x^{2}y.
Question 3: Find the greatest common factor (GCF/HCF) of the following polynomial:
7x, 21x^{2} and 14xy^{2}
Answer 3: The numerical coefficients of the given monomials are 7, 21 and 14. The greatest common factor of 7, 21 and 14 is 7.
The common literal appearing in the three monomials is x.
The smallest power of x in the three monomials is 1.
The monomial of the common literals with the smallest powers is x.
Hence, the greatest common factor is 7x.
Question 4: Find the greatest common factor (GCF/HCF) of the following polynomial:
42x^{2}yz and 63x^{3}y^{2}z^{3}
Answer 4: The numerical coefficients of the given monomials are 42 and 63. The greatest common factor of 42 and 63 is 21.
The common literals appearing in the two monomials are x, y and z.
The smallest power of x in the two monomials is 2.
The smallest power of y in the two monomials is 1.
The smallest power of z in the two monomials is 1.
The monomial of the common literals with the smallest powers is x^{2}yz.
Hence, the greatest common factor is 21x^{2}yz.
Question 5: Find the greatest common factor (GCF/HCF) of the following polynomial:
12ax^{2}, 6a^{2}x^{3} and 2a^{3}x^{5}
Answer 5: The numerical coefficients of the given monomials are 12, 6 and 2. The greatest common factor of 12, 6 and 2 is 2.
The common literals appearing in the three monomials are a and x.
The smallest power of a in the three monomials is 1.
The smallest power of x in the three monomials is 2.
The monomial of common literals with the smallest powers is ax^{2}.
Hence, the greatest common factor is 2ax^{2}.
Question 6: Find the greatest common factor (GCF/HCF) of the following polynomial:
9x^{2}, 15x^{2}y^{3}, 6xy^{2} and 21x^{2}y^{2}
Answer 6: The numerical coefficients of the given monomials are 9, 15, 6 and 21. The greatest common factor of 9, 15, 6 and 21 is 3.
The common literal appearing in the three monomials is x.
The smallest power of x in the four monomials is 1.
The monomial of common literals with the smallest powers is x.
Hence, the greatest common factor is 3x.
Question 7: Find the greatest common factor (GCF/HCF) of the following polynomial:
4a^{2}b^{3}, −12a^{3}b, 18a^{4}b^{3}
Answer 7: The numerical coefficients of the given monomials are 4, -12 and 18. The greatest common factor of 4, -12 and 18 is 2.
The common literals appearing in the three monomials are a and b.
The smallest power of a in the three monomials is 2.
The smallest power of b in the three monomials is 1.
The monomial of the common literals with the smallest powers is a^{2}b.
Hence, the greatest common factor is 2a^{2}b.
Question 8: Find the greatest common factor (GCF/HCF) of the following polynomial:
6x^{2}y^{2}, 9xy^{3}, 3x^{3}y^{2}
Answer 8: The numerical coefficients of the given monomials are 6, 9 and 3. The greatest common factor of 6, 9 and 3 is 3.
The common literals appearing in the three monomials are x and y.
The smallest power of x in the three monomials is 1.
The smallest power of y in the three monomials is 2.
The monomial of common literals with the smallest powers is xy^{2}.
Hence, the greatest common factor is 3xy^{2}.
Question 9: Find the greatest common factor (GCF/HCF) of the following polynomial:
a^{2}b^{3}, a^{3}b^{2}
Answer 9: The common literals appearing in the three monomials are a and b.
The smallest power of x in the two monomials is 2.
The smallest power of y in the two monomials is 2.
The monomial of common literals with the smallest powers is a^{2}b^{2}.
Hence, the greatest common factor is a^{2}b^{2}.
Question 10: Find the greatest common factor (GCF/HCF) of the following polynomial:
36a^{2}b^{2}c^{4}, 54a^{5}c^{2}, 90a^{4}b^{2}c^{2}
Answer 10: The numerical coefficients of the given monomials are 36, 54 and 90. The greatest common factor of 36, 54 and 90 is 18.
The common literals appearing in the three monomials are a and c.
The smallest power of a in the three monomials is 2.
The smallest power of c in the three monomials is 2.
The monomial of common literals with the smallest powers is a^{2}c^{2}.
Hence, the greatest common factor is 18a^{2}c^{2}.
Question 11: Find the greatest common factor (GCF/HCF) of the following polynomial:
x^{3}, − yx^{2}
Answer 11: The common literal appearing in the two monomials is x.
The smallest power of x in both the monomials is 2.
Hence, the greatest common factor is x^{2}.
Question 12: Find the greatest common factor (GCF/HCF) of the following polynomial:
15a^{3}, − 45a^{2}, − 150a
Answer 12: The numerical coefficients of the given monomials are 15, -45 and -150. The greatest common factor of 15, -45 and -150 is 15.
The common literal appearing in the three monomials is a.
The smallest power of a in the three monomials is 1.
Hence, the greatest common factor is 15a.
Question 13: Find the greatest common factor (GCF/HCF) of the following polynomial:
2x^{3}y^{2}, 10x^{2}y^{3}, 14xy
Answer 13: The numerical coefficients of the given monomials are 2, 10 and 14. The greatest common factor of 2, 10 and 14 is 2.
The common literals appearing in the three monomials are x and y.
The smallest power of x in the three monomials is 1.
The smallest power of y in the three monomials is 1.
The monomial of common literals with the smallest powers is xy.
Hence, the greatest common factor is 2xy.
Question 14: Find the greatest common factor (GCF/HCF) of the following polynomial:
14x^{3}y^{5}, 10x^{5}y^{3}, 2x^{2}y^{2}
Answer 14: The numerical coefficients of the given monomials are 14, 10 and 2. The greatest common factor of 14, 10 and 2 is 2.
The common literals appearing in the three monomials are x and y.
The smallest power of x in the three monomials is 2.
The smallest power of y in the three monomials is 2.
The monomial of common literals with the smallest powers is x^{2}y^{2}.
Hence, the greatest common factor is 2x^{2}y^{2}.
Question 15: Find the greatest common factor of the terms in each of the following expression:
5a^{4}^{ }+ 10a^{3} − 15a^{2}
Answer 15: Terms are expressions separated by plus or minus signs. Here, the terms are 5a^{4}, 10a^{3} and 15a^{2}.
The numerical coefficients of the given monomials are 5, 10 and 15. The greatest common factor of 5, 10 and 15 is 5.
The common literal appearing in the three monomials is a.
The smallest power of a in the three monomials is 2.
The monomial of common literals with the smallest powers is a^{2}.
Hence, the greatest common factor is 5a^{2}.
Question 16: Find the greatest common factor of the terms in each of the following expression:
2xyz + 3x^{2}y + 4y^{2}
Answer 16: The expression has three monomials: 2xyz, 3x^{2}y and 4y^{2}.
The numerical coefficients of the given monomials are 2, 3 and 4. The greatest common factor of 2, 3 and 4 is 1.
The common literal appearing in the three monomials is y.
The smallest power of y in the three monomials is 1.
The monomial of common literals with the smallest powers is y.
Hence, the greatest common factor is y.
Question 17: Find the greatest common factor of the terms in each of the following expression:
3a^{2}b^{2} + 4b^{2}c^{2} + 12a^{2}b^{2}c^{2}
Answer 17: The expression has three monomials: 3a^{2}b^{2}, 4b^{2}c^{2} and 12a^{2}b^{2}c^{2}.
The numerical coefficients of the given monomials are 3, 4 and 12. The greatest common factor of 3, 4 and 12 is 1.
The common literal appearing in the three monomials is b.
The smallest power of b in the three monomials is 2.
The monomial of common literals with the smallest powers is b^{2}.
Hence, the greatest common factor is b^{2}.