Question

Use Eclid's method to determine the GCF of 24 and 60. Use the GCF and the distributive property to add 24 + 60.

Answer 1

12 is the GCF

GCF and the distributive property = 84

Explanation:

GCFof 24 and 60

Using the Euclid's method:

First we divide 60 by 24:

$\begin{gathered} \frac{60}{24}=2\text{ remainder }12 \\ 24(2)\text{ + 12 = }60 \end{gathered}$

Then we divide 24 by the remainder 12:

$\begin{gathered} \frac{24}{12}=\text{ 2 remainder 0} \\ 12(2)\text{ + 0 = 24} \end{gathered}$

Since there are no more remainders, the number which we divided by another that produced a remainder of zero is the GCF (greatest common factor)

We divided 24 by 12 to produce a remainder of 0. The divisor is 12

Hence, 12 is the GCF

Using property to add 24 + 60:

we check for the greatest number common to both

12 is the greatest common factor to both

24 = 2(12)

60 = 12(5)

24 + 60 = 12(2 + 5)

= 12(7)

= 84