What is the greatest common factor of $16 and 30$ $16 and 30$ ?

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Answer 1 · 2018-03-04T19:26:18

See a solution process below:

First, factor each of the numbers as:

$16 = 2 \times 2 \times 2 \times 2$ $16 = 2 xx 2 xx 2 xx 2$

$30 = 2 \times 3 \times 5$ $30 = 2 xx 3 xx 5$

Next, identify the common factors for each number:

$16 = 2 \times 2 \times 2 \times 2$ $16 = color(red)(2) xx 2 xx 2 xx 2$

$30 = 2 \times 3 \times 5$ $30 = color(red)(2) xx 3 xx 5$

$GCF = 2$ $"GCF" = color(red)(2)$

Answer 2 · 2018-03-04T19:29:18

2

Use trial and error to go through each possible factor:

2: $\frac{16}{2} = 8$ $16/2 = 8$ and $\frac{30}{2} = 15$ $30/2 = 15$ so 2 is a factor. Let's keep going up

3: Can't divide 16 by 3 to get a whole number so 3 is not a common factor even if it is for 30

4: Can't divide 30 by 4 to get a whole number so 4 is not a common factor

5: Can't divide 16 by 5 to get a whole number so 5 is not a common factor

These are the main numbers you test if the answer doesn't seem obvious. As 2 was the largest factor we got, it's the answer.

What is the greatest common factor of 16and3016 and 30?