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
•
Total views: 306.6k
•
Views today: 5.85k
Answer
306.6k+ views
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.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India
