What is the greatest common factor of 8x and 40?

2 answers:

7 0

ANSWER

The greatest common factor is
$8$

EXPLANATION

We want to find the greatest common factor of
$8x \: and \: 40.$

We use prime factorization to find the greatest common factor of
$8x \: \: and \: \: 40.$

The prime factorization of 8x is,

$8x = {2}^{3} \times x$

The prime factorization of 40 is

$40 = {2}^{3} \times 5$

The greatest common factor of 8x and 40 is

${2}^{3} = 8$

satela [25.4K]2 years ago

3 0

The GCF of 8x and 40 is 8.

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Youssef can either way from his home to his workplace or ride his bicycle. he walks at a pace of 1 block per min, but he can tra

alex41 [277]

Youssef lives 15 blocks away from his work

Solution:

Given that Youssef can either way from his home to his workplace or ride his bicycle

Let "x" be number of blocks away from work Youssef works

Case 1: walking

He walks at a pace of 1 block per min

Therefore,

1 block = 1 minute

Thus to cross "x" blocks he takes "x" minutes

Case 2: Bicycle

He can travel 1 block in 20 sec on his bicycle

We know that,

To convert seconds to minute, divide the time value by 60

$\rightarrow 20 seconds = \frac{20}{60} minutes = \frac{1}{3} minutes$

Thus he takes 1/3 minutes for 1 block

So to cross "x" blocks he will take $\frac{x}{3}$ minutes

Given that it takes youssef 10 min longer to walk to work than to ride his bike

This means difference between time taken to cross "x" blocks by walking and ride by bicycle is 10 minutes

$\rightarrow x - \frac{x}{3} = 10\\\\\rightarrow \frac{3x - x}{3} = 10\\\\\rightarrow \frac{2x}{3} = 10\\\\\rightarrow x = \frac{30}{2}\\\\\rightarrow x = 15$