HCF of (176,38220) by division algorithm ?

Question

Answer

Answer

BY E.D LEMMA ,

38220 = 176 × 217 + 28

=> 176 = 28 × 6 + 8

=> 28 = 8 × 3 + 4

=> 8 = 4 × 2 + 0

Hence , we got the remainder is zero..and 4 as last divisor. Therefore, H.C.F ( 176 , 38220 ) = 4.

Answer

Division Algorithm to Find HCF

To find the highest common factor (HCF) of two numbers using the division algorithm, we need to perform a series of divisions until we reach a remainder of zero. The HCF is the last non-zero remainder obtained in this process. Let's apply the division algorithm to find the HCF of 176 and 38220.

Step 1: Divide the larger number by the smaller number

In this case, 38220 is the larger number and 176 is the smaller number.

Dividing 38220 by 176 gives us:
38220 ÷ 176 = 217 with a remainder of 52

Step 2: Divide the divisor (176) by the remainder (52)

Now, we divide 176 by 52:
176 ÷ 52 = 3 with a remainder of 20

Step 3: Divide the previous remainder (52) by the new remainder (20)

We divide 52 by 20:
52 ÷ 20 = 2 with a remainder of 12

Step 4: Divide the previous remainder (20) by the new remainder (12)

Continuing the process, we divide 20 by 12:
20 ÷ 12 = 1 with a remainder of 8

Step 5: Divide the previous remainder (12) by the new remainder (8)

Lastly, we divide 12 by 8:
12 ÷ 8 = 1 with a remainder of 4

Step 6: Divide the previous remainder (8) by the new remainder (4)

Dividing 8 by 4 gives us:
8 ÷ 4 = 2 with a remainder of 0

Since the remainder is now zero, we stop the process. The HCF of 176 and 38220 is the last non-zero remainder obtained, which is 4.

HCF(176, 38220) = 4

Summary:

Using the division algorithm, we divided the larger number (38220) by the smaller number (176) and obtained a remainder of 52. Then, we continued dividing the previous divisor by the new remainder until we reached a remainder of zero. The last non-zero remainder obtained was 4, which is the highest common factor of 176 and 38220.

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