Question

The HCF a of 2021 and 2022​

Answer 1

Answer:

1

Step-by-step explanation:

Concept= HCF using Euclid's Division

Given= Two Numbers

To Find= The HCF

Explanation=

We have been told to find the HCF of 2021 and 2022.

HCF= Highest Common Factor or Greatest Common Divisor.

Such a number which divides both the numbers leaving remainder 0.

Here we will apply the Euclid's Division Algorithm to find the HCF of 2021 and 2022.

Euclid's Division Lemma states that out of given two numbers  a and b where a>b the division algorithm is a=bq + r

q and r is the quotient and remainder.

When the remainder becomes 0(zero) the divisor is the HCF of the two numbers.

Applying the algorithm to 2021 and 2022

since 2022>2021 so

2022= 2021*1 +1

Here the remainder is not 0 so we now apply the algorithm to 1 and 2021

2021 = 1*2021 + 0.

Now we have got the remainder 0 and the divisor is 1. So, the HCF of the two numbers is 1.

HCF of 2021 and 2022 is 1.

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Answer 2

Answer:

The Answer is 1

Step-by-step explanation:

HCF is the Highest Common Factor of two or more numbers. Essentially it is the greatest number which divides two or more numbers.

We can find the HCF of smaller numbers by simply dividing however for larger numbers, we use Euclid's Theorem to find the HCF of the numbers.

$a=bq+r$

Here, a is the bigger number, b is smaller number, q is the quotient and r is the remainder.

By applying the theorem,

$2022 = 2021 * 1 + 1$

Hence, 1 is the HCF of the numbers.

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