Question

Write the following monomials as product and find their common factors.

(1) 4p²q, 16pq²
(2) 18x³y², 12x³y
(3) 7a³b²c, 28a²bc²
(4) 8x³y², 10x²y³, 6x²y
(5) 24mnp², 22m²p², 30m²n²p

Answer 1

(1) 4p²q, 16pq²
4p²q = 2 × 2 × p × q × q
16pq² = 2 × 2 × 2 × 2 × p × q × q
Hence, the common factors are 2 × 2 × p × q = 4pq .

(2) 18x³y², 12x³y
18x³y² = 2 × 3 × 3 × x × x × x × y × y
12x³y = 2 × 2 × 3 × x × x × x × y
Hence, the common factors are 2 × 3 × x × x × x × y = 6x³y .

(3) 7a³b²c, 28a²bc²
7a³b²c = 7 × a × a × a × b × b × c
28a²bc² = 2 × 2 × 7 × a × a × b × c × c
Hence, the common factors are 7 × a × a × b × c = 7a²bc .

(4) 8x³y², 10x²y³, 6x²y
8x³y² = 2 × 2 × 2 × x × x × x × y × y
10x²y³ = 2 × 5 × x × x × y × y × y
6x²y = 2 × 3 × x × x × y
Hence, the common factors are 2 × x × x × y = 2x²y .

(5) 24mnp², 22m²p², 30m²n²p
24mnp² = 2 × 2 × 2 × 3 × m × n × p × p
22m²p² = 2 × 11 × m × m × p × p
30m²n²p = 2 × 3 × 5 × m × m × n × p
Hence, the common factors are 2 × m × p = 2mp .