Question

Select all the expressions that have a greatest common factor (GCF) of 3xy^2 with 42xy^4.
A. 6x^2y^2
B. 15xy^2z
C. 27x^3y^2
D. 9xy^3
E. 21xy^2

Answer 1

Answer:

B and C

Step-by-step explanation:

GCF is the highest common factor of two or more expression.

The GCF of

$6 {x}^{2} {y}^{2} \: \: and \: \: 42x{y}^{4} \: is \: 6x {y}^{2}$

The GCF of

$15x {y}^{2} z \: \: and \: \: 42x {y}^{4} \: \: is \: 3x {y}^{2}$

The GCF of

$27 {x}^{3} {y}^{2} \: \: and \: \: 42x {y}^{4} \: is \: \: 3x {y}^{2}$

The GCF of

$9x {y}^{3} \: and \: 42x {y}^{4} \: is \: 3x {y}^{3}$

The GCF of

$21x {y}^{2} \: and \: 42x {y}^{4} \: \: is \: \: 7x {y}^{2}$

Therefore

$15x{y}^{2} z \: \: and \: 27 {x}^{3} {y}^{2}$

have a GCF of

$3x {y}^{2}$

with

$42x {y}^{4}$

Option B and C are correct

Answer 2

The expressions that have a greatest common factor (GCF) of 3xy² with 42xy⁴ is 15xy²z

The Greatest Common Factor is the highest number that divides exactly into two or more numbers with zero remainder.

42xy⁴ = 2 * 3 * 7 * x * y * y * y * y

6x²y² = 2 * 3 * x * x * y * y

15xy²z = 3 * 5 * x * y * y * z

27x³y² = 3 * 7 * x * x * x * y * y

9xy³ = 3 * 3 * x * y * y * y

21xy² = 3 * 7 * x * y * y

The expressions that have a greatest common factor (GCF) of 3xy² with 42xy⁴ is 15xy²z

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