This topic would discuss about finding highest common factor using the division method. We have already learnt finding the highest common factor by prime factorization method but it is not suitable when we are dealing with large numbers. Division method is quite convenient when we are finding the highest common factor of large numbers.
Steps involved in finding highest common factor using division method:
Step I: The larger number is divided by the smaller number
Step II: The remainder of the division in step 1 is the new divisor for next division and the divisor of the previous division is the dividend
Step III: Divide the new dividend by the new divisor (as ascertained in step 1)
Step IV: Again repeat the same process as explained in step 2 i.e. the remainder of step 3 will become the new divisor for next division and the divisor of the previous division is the dividend
Step V: In this way carry on the division until the remainder is 0
Step VI: The division where the remainder becomes 0 is the last step of the process and the divisor of that last division is the Highest common factor or H. C. F
Here are a few examples to illustrate finding highest common factor using division method:
1. Find the Highest Common factor of 560 and 1020 by using division method
Solution:
Highest common factor of 560 and 1020 is 20
Step I:
Dividing 1020 by 560 and we get remainder 460
Step II:
Then the remainder of Step 1 becomes the divisor and the divisor of Step 1 become the dividend and 100 is the remainder
Step III:
Now 100 is the divisor and 460 is the dividend. Hence 460 is divided by 100
Step IV:
Again 100 the divisor of previous step is divided by the remainder (i.e. 60) of the previous step.
Step V:
Again 60 the divisor of previous step is divided by the remainder (i.e. 40) of the previous step.
Step VI:
Now 20 is the remainder of previous step is treated as the divisor and the divisor that is 40 of the previous step is treated as dividend and the remainder is zero.
Hence the last divisor is 20 and that is the Highest common factor
2. Find the Highest Common factor of 80 and 120 by using division method
Solution:
Highest common factor of 80 and 120 is 40
Step I:
Dividing 120 by 80 and we get remainder 40
Step II:
Then 40 becomes the divisor and 80 becomes the dividend and the remainder is 0
Step III:
The highest common factor is the divisor of the last division that is 40
3. Find the Highest Common factor of 32 and 128 by using division method
Solution:
Highest common factor of 32 and 128 is 32
This example shows that there is no repeated division hence in that case as well the first divisor will become the highest common factor.
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