# What will be the HCF of two numbers that are consecutive and belong to the set of natural numbers?

Last updated date: 25th Mar 2023

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Hint:- Assume that two numbers x and x + 1 are consecutive natural numbers. And then find the HCF of x and x + 1.

Complete step-by-step answer:

As we know that natural numbers are the sets of numbers starting from 1 and goes on till infinity.

Natural numbers are {1, 2, 3, 4, ………………}

And consecutive numbers are the numbers with difference 1.

So, let x be any natural number.

Then, the other natural number consecutive to x will be x + 1.

We had to find HCF of x and x + 1.

Now, as we know that HCF of two numbers is the greatest possible number that is the common factor of both the numbers.

But here the difference of the two numbers is 1.

So, the common factor of x and x + 1 can only be one.

So, 1 will be the greatest number by which x and x + 1 can both be divided exactly.

Hence, the HCF of x and x + 1 will be 1.

Note:- Whenever we are given two numbers and asked to find HCF of two numbers then there can be two methods to find the HCF of the given numbers. In the first method we perform division till we get the remainder equal to zero. And in another method we first, find the set of all the factors of both numbers and then find that factor that is common to both the sets of factors. After that multiply all common factors to get the HCF of the numbers.

Complete step-by-step answer:

As we know that natural numbers are the sets of numbers starting from 1 and goes on till infinity.

Natural numbers are {1, 2, 3, 4, ………………}

And consecutive numbers are the numbers with difference 1.

So, let x be any natural number.

Then, the other natural number consecutive to x will be x + 1.

We had to find HCF of x and x + 1.

Now, as we know that HCF of two numbers is the greatest possible number that is the common factor of both the numbers.

But here the difference of the two numbers is 1.

So, the common factor of x and x + 1 can only be one.

So, 1 will be the greatest number by which x and x + 1 can both be divided exactly.

Hence, the HCF of x and x + 1 will be 1.

Note:- Whenever we are given two numbers and asked to find HCF of two numbers then there can be two methods to find the HCF of the given numbers. In the first method we perform division till we get the remainder equal to zero. And in another method we first, find the set of all the factors of both numbers and then find that factor that is common to both the sets of factors. After that multiply all common factors to get the HCF of the numbers.

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