The exercise includes the use of Euclids division lemma.
Que1
Use Euclid division algorithm to find HCF of:
1: 135 and 225
2:196 and 38220
3: 867 and 225
Solution:
1: 135 and 225
Here we can see that 225 is greater than 135. Therefore applying Euclid division algorithm we can have,
225 = 135*1 +90
Again remainder 90 is not equal to zero, so we can apply Euclid division lemma for 90 and we get,
135=90*1+45
Again 45 is not equal to zero, repeating the step we have,
90=45*2+0
Here we get remainder zero, and in the last step divisior is 45 therefore we get our hcf.
Hence HCF of 135 and 225 is 45.
2: 196 and 38220
Here 38220 > 196 therefore by applying division lemma and taking 38220 as divisor, we get
38220 = 196*195+0
Remainder is zero.
The HCF is 196.
3: 867 and 225
Here 867 > 225 ,therefore by applying division lemma and taking 867 as divisor we get,
867 =225*3+102
But we don’t get remainder zero therefore by applying Euclid division algorithm and taking 102 as a divisor we get,
225 =102*2+51
Again remainder is not equal to zero so repeating the process we get,
102 = 51*2+0
Now we get the remainder zero.
Hence HCF is 51.
