Question

3. Find the HCF of 1001 and 385 using Euclid’s division algorithm.

Answer 1

Answer:

77

Step-by-step explanation:

The highest common factor of two numbers is the largest possible number which divides both the numbers exactly without any remainder.

We will use the following two methods to find the HCF of 1001 and 385.

HCF of 1001 and 385 by Long Division Method

HCF of 1001 and 385 by Listing Method

Method 1: HCF of 1001 and 385 by Long Division

Step 1: Divide 1001 by 385 and check the remainder.

Step 2: Make the remainder (231) of the above step as the divisor and the divisor (1001) of the above step as the dividend and perform the long division again.

Step 3: Continue the same process of step 1 & step 2till you get the remainder as 0 and the last divisor of the division process is the HCF of 1001 and 385.

HCF of 1001 and 385 by division method

So, the highest common factor of 1001 and 385 is 77

Method 2: HCF of 1001 and 385 by Listing the Common Factors

In this method, we list all the factors of 1001 and 385, then identify the common factors.

The highest among the common factors is the HCF of 1001 and 385.

Factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001

Factors of 385 are 1, 5, 7, 11, 35, 55, 77, 385

The common factors of 1001 and 385 are 1, 7, 11, and 77

So, the highest common factor of 1001 and 385 is 77

HCF of 1001 and 385 is 77

The HCF of 1001 and 385 remains the same, irrespective of the method we opt for.

Thus, the highest common factor (HCF) of 1001 and 385 is 77

Hope it helps