Question

Use Euclid’s algorithm to find the greatest common factor of the following pairs of numbers:

a. GCF (12, 78)
b. GCF (18, 176)

Answer 1

The GCF (12, 78) is 6 and GCF (18, 176) is 2.

Explanation:

Step 1:

The greatest common factor of the number is defined as the factor of two or more numbers. The acronym of Greatest common factor is GCF.

(a)

GCF (12, 78)

The greatest common factor of the two numbers 12 and 78 is calculated by Euclid’s algorithm as follows:

`78=12*6+6`

`12=6*2+0`

Therefore, the greatest common factor GCF is 6.

Step 2:

(b)

GCF (18, 176)

The greatest common factor of the two numbers 18 and 176 is calculated by Euclid’s algorithm as follows:

`176=18*9+14`

`18=14*1+4`

`14=4*3+2`

`4=2*2+0`

Therefore, the greatest common factor GCF is 2.