What is the GCF of 40xy and 24x? please help!!!!!!?

1. 8x
2. C. 9y(2x - 5z)

GCF of 40xy and 24x
i.e. GCF of 40x^1y^1 and 24 x^1 y^0
Take GCF of 40 and 24 by factors
40 = 8 × 5 and 24 = 8 × 3
GCF = 8
GCF of variables take lowest index of x and y
lowest index of x is x^1 = x
lowest index of y is y^0 = 1
Total GCF = 8x × 1 = 8x

GCF
18xy - 45yz
18 = 9 × 2
45 = 9 × 5
GCF of 18 and 45 = 8
18xy = 9 × 2 × x^1y^1z^0
45yz = 9 × 5 × x^0y^1z^1
Total GCF = 9 × x^0y^1z^0 = 9y
18xy - 45yz
= 9y(2xz^0 – 5x^0z^1)
= 9y(2x – 5z)
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Note that 40xy = 2X2X2X5 x y, and 24x = 2X2X2X3 x
both 'contain' 8 and x in common and no other's bigger. So 8x is the answer

In the second case: 9y*(2x - 5z), following the above.

1)
40xy = 2^3 * 5 * x * y
24x = 2^3 * 3 * x
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The GCF of 40xy and 24x is:
2^3 * x
= 8x
(answer A)

2)
18xy - 45yz
= 9(2xy - 5yz)
= 9y(2x - 5z)
(answer C)

A

Factor the expressions into primes.
40xy = 2³∙5∙x∙y
24x = 2³∙3∙x
(since you don't know otherwise, assume that x and y are primes)

Identify the factors common to both expressions: 2³ and x
GCF(40xy, 24x) = 2³x
= 8x
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Find the prime factors of the expressions.
18xy = 2∙3²∙x∙y
45xyz = 3²∙5∙x∙y∙z

Factors common to both expressions: 3², x, and y
GCF(18xy, 45xyz) = 3²xy
= 9xy

18xy - 45xyz = 9xy(2-5z)