Question

Find the common factors of the following monomials by inspection only.

(1) 6m²n², 10m²n
(2) 38a³b², 57ab²
(3) 11x²y³, xy²
(4) 35p²q²r, 40p³q², 50pq²r
(5) 15x³y³, 39x²z², 48xy²z³

Answer 1

(1) 6m²n², 10m²n
The highest common factor of 6 and 10 is 2
Common factor of m² and m² is m²
Common factor of n² and n is n
Hence, the common factor of the monomial 6m²n²and 10m²n is 2m²n

(2) 38a³b², 57ab²
The highest common factor of 38 and 57 is 19
Common factor of a³ and a is a
Common factor of b² and b² is b²
Hence, the common factor of the monomial 38a³b²and 57ab² is 19ab²

(3) 11x²y³, xy²
The highest common factor of 11 and 1 is 1
Common factor of x² and x is x
Common factor of y³ and y² is y²
Hence, the common factor of the monomial 11x²y³ and xy² is 1xy² = xy²

(4) 35p²q²r, 40q³r², 50pq²r
The highest common factor of 35, 40 and 50 is 5
Common factor of p², p⁰ and p is p⁰ = 1
Common factor of q², q³ and q² is q²
Common factor of r, r² and r is r
Hence, the common factor of the monomial 35p²q²r, 40q³r² and 50pq²r is 5 q²r

(5) 15x³y³, 39x²z², 48xy²z³
The highest common factor of 15, 39 and 48 is 3
Common factor of x³, x² and x is x
Common factor of y³, y⁰ and y² is y⁰ = 1
Common factor of z⁰, z² and z³ is z⁰ = 1
Hence, the common factor of the monomial 15x³y³, 39x²z² and 48xy²z³ is 3x (1) (1) = 3x