Example 1: Find out the HCF of 8 and 12.
Given data 
: Choose the highest number which is 12 in this case and assign it to a.
a = 12 (the highest number) b= 8
Find out 
: To find out the HCF.
Procedure 
: Using a = bq + r (Euclid´s division lemma) ( a = dividend, b= divisor, q= quotient, r = remainder)
a = b * q + r
12 = 8 * 1 + 4
Now b becomes a and r becomes b so a = 8 and b = 4.
since r = 0 , b = 4 is the HCF.
Solution 
: The HCF of 8 and 12 is 4.
Example 2: Find out the HCF of 4,052 and 12,576.
Given data : Choose the highest number which is 12,576 in this case and assign it to a.
a = 12,576(the highest number) b= 4,052
Find out : To find out the HCF.
Procedure : Using a = bq + r (Euclid´s division lemma) ( a = dividend, b= divisor, q= quotient, r = remainder)
a = b * q + r
12576 = 4052 * 3 + 420
Now b becomes a and r becomes b so
a = 4052 and b = 420
4052 = 420*9 +272
Now b becomes a and r becomes b so
a = 420 and b = 272
420 = 272 *1 + 148
Now b becomes a and r becomes b so
a = 272 and b = 148
272 = 148*1 + 124
Now b becomes a and r becomes b so
a = 148 and b = 124
148 = 124*1 + 24
Now b becomes a and r becomes b so
a = 124 and b = 24
124 = 24* 5 + 4
Now b becomes a and r becomes b so
a = 24 and b = 4
24 = 4*6 + 0
Since r = 0, b = 4 is the HCF.
Solution : The HCF of 4,052 and 12,576 is 4.
| Given data : Choose the highest number between 600 and 36 and assign it to a. So a = = (highest number) and b = (the other number). |
| Find out : To find out the hcf. |
| Procedure : Using a = bq + r (Euclid´s division lemma ) where (a = dividend, b= divisor, q = quotient and r= remainder). |
| = q |
 |
| b = = a –  – = r |
| a = b * q + r = * + |
| Now b becomes a and r becomes b. So a = and b = . |
| = q |
|
| b = = a – = r |
| a = b * q + r = * + |
| Now b becomes a and r becomes b. So a = and b = . |
| = q |
|
| b = = a – = r |
| a = b * q + r = * + |
| Since r = 0 , b = is the HCF. |
| Solution : The HCF of 600 and 36 is . |