HCF by Division Method

Long division is a way of splitting big numbers into groups or portions that is used in mathematics. Long division aids in the division challenge being broken down into a series of simpler phases. A large number, the dividend, is divided by a smaller number, the divisor, to produce a quotient and, occasionally, a remainder, as in all division problems. Basic math operations are used in long division.

This method involves drawing a tableau to divide two numbers. The divisor appears outside of the right parenthesis, whereas the dividend appears inside. Above the over bar and on top of the dividend, the quotient is inscribed.

Here is how to use the division method to determine the highest common factor.

It’s not easy to find the highest common factor (H.C.F.) for a large integer using prime factorization. When dealing with huge numbers, the long division method is more useful.

We divide the larger number by the smaller number first in this procedure. The remainder is the new divisor, with the prior divisor serving as the new dividend. We keep going till there is no more leftover.

The highest common factor (H.C.F) of two or more numbers is found using the repeated division method.

Step 1: Take the larger number and divide it by the smaller number.

Step 2: The remainder is then handled as a divisor, and the divisor is treated as a dividend.

Step 3: Take the first remainder and divide it by the first divisor.

Step IV: Subtract the remainder from the second divisor.

Step V: Repeat steps 1-4 until the remaining equals zero.

Step VI: The last divisor is the required highest common factor (H.C.F) of the given integers because it does not leave a remainder.

Follow these procedures to calculate the HCF using the division method:

Step 1: Divide the larger number by the smaller amount and examine the remainder.

Step 2: Divide the dividend by the remainder of the previous step.

Step 3: Keep dividing till the remainder is not zero.

Step 4: The HCF of the input integers will be the final divisor.

Let’s have a look at an example of this procedure.

Let’s look at several instances to see how we may use the division approach to find the highest common factor (H.C.F).

Divide the numbers 18 and 30 to find the highest common factor (H.C.F).

Step 1: Identify the problem. 

Here we need to divide 30 by 18. 

[Subtract the greater number from the smaller].

Step II:

We must divide 18 by 12 because the first divisor is 18 and the remainder is 12.

[Subtract the first remainder from the first divisor].

Step III:

Divide the second remainder 6 by the second divisor 12.

[Subtract the second remainder from the second divisor].

Step IV:

The remainder equals zero.

Step V:

As a result, the highest common factor is 6.

[The required highest common factor (H.C.F) of the given numbers is the last divisor.]

Using the division method, find the highest common factor (H.C.F) of 75 and 180.

Step 1 of the solution:

We must divide 180 by 75 in this case.

[Subtract the greater number from the smaller].
Step 2: We need to divide 75 by 30 because the first divisor is 75 and the remainder is 30.

[Subtract the residual from the first divisor].

Step 3: Subtract the second remainder 15 from the second divisor 30.

[Take the second remainder and divide it by the second divisor.]

Step 4: The residue is reduced to zero.

Step 5: As a result, the greatest common factor is equal to 15.

[The highest common factor (H.C.F) of the provided numbers is the last divisor.]

Conclusion 

Following the procedures below, we can find the HCF of the given numbers using the division method:

Check the remainder after dividing the two numbers (bigger number by smaller number).

Make the divisor the remainder of the previous step, and the dividend the divisor of the previous step, then divide once more.

Continue dividing until the remainder is equal to 0.

The HCF of the two numbers will be the last divisor.

The following procedures are followed to find the LCM of the given numbers using the division method:

Step 1: Subtract the least prime number from the total.

Step 2: Following the numbers in the next row, write the quotients.

Step 3: Assume the above quotients as fresh dividends for the following division step.

Step 4: Consider another prime number that divides at least one of the dividends precisely.

Step 5: Continue in this manner until we get 1 in the last row.

To find the LCM of the given numbers, multiply all the prime numbers on the left hand side of the bar.