# the sum of three consecutive numbers is always divisible by

### Mohammed

Guys, does anyone know the answer?

get the sum of three consecutive numbers is always divisible by from screen.

## [Solved] The sum of three consecutive integers is always divisib

Sum of three consecutive integers is always divisible by 6. For ex: Let three consecutive integers be 21, 22 and 23. Sum = 66, which is divisible by 6.

Home Quantitative Aptitude Number System Divisibility and Remainder

## Question

Download Solution PDF

## The sum of three consecutive integers is always divisible by ____.

This question was previously asked in

SSC CPO Tier- I Previous Paper 8 (Held on: 4th July 2017 Shift 2)

Download PDF Attempt Online

View all SSC CPO Papers >

12 6 18 24

## Answer (Detailed Solution Below)

Option 2 : 6 Crack Railway with

India's Super Teachers

FREE

Demo Classes Available*

Explore Supercoaching For FREE

**Free Tests**

View all Free tests >

FREE Cell 6.6Lac Users

10 Questions 10 Marks 7 Mins

Start Now

## Detailed Solution

Download Solution PDF

Sum of three consecutive integers is always divisible by 6.

For ex:

Let three consecutive integers be 21, 22 and 23.

Sum = 66, which is divisible by 6.

Download Solution PDF

Share on Whatsapp

Latest RRB NTPC Updates

Last updated on Sep 21, 2022

The RRB (Railway Recruitment Board) has released the Result, and Cut Off marks for the CBAT (Computer Based Aptitude Test) stage for Pay Level 6. The result and cut-off marks are announced for the RRB Chandigarh, Bhopal & Chennai regions for the recruitment cycle 2021. The exam is conducted to fill up a total number of 35281 vacant posts. Candidates who are qualified for the Computer Based Aptitude Test will be eligible for the next round, which will be Document Verification & Medical Exam. The candidates with successful selection under RRB NTPC will get a salary range between Rs. 19,900 to Rs. 35,400. Know the RRB NTPC Result here.

India’s **#1 Learning** Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free

Download App

Trusted by 3,17,93,763+ Students

‹‹ Previous Ques Next Ques ››

## More Divisibility and Remainder Questions

**Q1.**If an 8-digit number 1862383A is divisible by 22, find the value of A.

**Q2.**Find the greatest value of k for which the 6-digit number 24312k is divisible by 6.

**Q3.**If an 8-digit number 256139A4 is divisible by 11, find the value of A.

**Q4.**Find the greatest value of (a + b) such than an 8-digit number 4523a60b is divisible by 15.

**Q5.**Given below are two statements Statement I: If two numbers divided by a third number give the same remainder, their difference is exactly divisible by that number. Statement II: Least common multiple of two or more given numbers is the largest number which is exactly divisible by each of them. In light of the above statements, choose the correct answer from the options given below

**Q6.**Let p = 22n + 2 + m and q = 24n - m (where n is even natural number). What should be the least value of m such that p as well as q is divisible by 5?

**Q7.**275 + 313 is divisible by

**Q8.**461 + 462 + 463 + 464 is divisible by

**Q9.**4143 + 4343 is divisible by

**Q10.**What is the number of divisors of 1000 (excluding 1 and 1000)?

## More Number System Questions

**Q1.**If an 8-digit number 1862383A is divisible by 22, find the value of A.

**Q2.**The least number by which 72 must be multiplied in order to produce a multiple of 112 is

**Q3.**In a school there are 360, 520 and 280 students in classes 5, 6 and 7 respectively. Buses are to be hired to take these students for a trip. Find the maximum number of students who can be accommodated in each bus if each bus must take same number of students, and each bus should have students from the same class.

**Q4.**Find the greatest value of k for which the 6-digit number 24312k is divisible by 6.

**Q5.**Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

**Q6.**If an 8-digit number 256139A4 is divisible by 11, find the value of A.

**Q7.**If 23.5% of a number is 11.75, then what is the number?

**Q8.**If x =

2+32−3

, then the value of (x - 7)2 is

**Q9.**Find the greatest value of (a + b) such than an 8-digit number 4523a60b is divisible by 15.

**Q10.**If the square of a positive number is 6 more than five times the number, what is the number?

## The sum of three consecutive numbers is always divisible by 4. Ver

The sum of three consecutive numbers is always divisible by 4. Verify this statement with the help of some examples.

Previous Question Next Question Question :

## The sum of three consecutive numbers is always divisible by 4. Verify this statement with the help of some examples.

Answer :

## 3 + 5 = 8 and 8 is divisible by 4.5 + 7 = 12 and 12 is divisible by 4.7 + 9 = 16 and 16 is divisible by 4.9 + 11 = 20 and 20 is divisible by 4.

Related Answer

The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

More Related Question & Answers

3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES 3.0k LIKES 3.0k VIEWS 1.5k SHARES

## The sum of three consecutive odd numbers is always class 8 maths CBSE

The sum of three consecutive odd numbers is always divisible by A 1 B 3 C 5 D 6

The sum of three consecutive odd numbers is always divisible byA) 1 B) 3 C) 5 D) 6 Answer Verified 201.6k+ views

**Hint**: The consecutive odd numbers refer to the numbers taken in a continuous manner skipping events in between. We can assume 3 such numbers using a variable, take their sum and see what number can we get common because that will be the one by which the sum will always be divisible

**Complete step-by-step answer**:

Some consecutive odd numbers are:

1, 3, 5, 7

We can see that the gap between two consecutive odd numbers is 2. Let us assume three consecutive numbers to be:

n n+2 n+2+2 ⇒(n,n+2,n+4)

nn+2n+2+2⇒(n,n+2,n+4)

The sum of these three odd consecutive numbers is given as:

n+n+2+n+4=3n+6 n+n+2+n+4=3n+6

From this sum, we can take number 3 as common:

(3n+6)⇒3(n+2) (3n+6)⇒3(n+2)

This shows that the answer will be a product of 3, n be any number. Thus, the same will be divisible by 3.

Therefore, the sum of three consecutive odd numbers is always divisible by 3 and the correct answer is

3 3 .

**So, the correct answer is “Option B”.**

**Note**: The natural numbers (greater than 1) are odd and even in an alternative manner and thus consecutive events and odds respectively are at a gap of two.

We can check if the answer obtained is correct or not by taking an example.

If the three consecutive integers are 3, 5, 7, their sum will be:

3+5+7=15 3+5+7=15

And 15 is the product of 3 and 5 and thus is divisible by both.

If the three consecutive integers are 11, 13, 15, their sum will be:

11+13+15=39 11+13+15=39

And 39 is the product of 3 and 11 and thus is divisible by both.

The common number by which both the sums are divisible is 3 so the answer we obtained is correct.

Prepare better for CBSE Class 8

Try Vedantu PRO for free

LIVE classes with top teachers

In-class doubt-solving

Practice tests and quizzes

Latest Vedantu courses for you

Grade 8 | CBSE | SCHOOL | English

Class 8 CBSE 2022-23

Academic year 2022-23

ENGLISH

Unlimited access till final school exam

School Full course for CBSE students

500+ chapter specific short courses

Maths Science English ₹9,000 per year Select and buy

Recently Updated Pages

If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

The coordinates of the points A and B are a0 and a0 class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

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

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

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

Name the Largest and the Smallest Cell in the Human Body ?

Related Questions Question 1 Smallest 6 6

digit number divisible by

6 6 is ___________. A. 100000 100000 B. 100002 100002 C. 100003 100003 D. 100004 100004 Question 2

A number is divisible by

8 8

if the number formed by the digit in .….. placed is divisible by

8 8 . (A) units and tens

(B) tens and hundred

(C) units

(D) units, tens and hundred

Question 3

Which of the following numbers is exactly divisible by 99?

A. 114345 B. 135792 C. 3572404 D. 913464 Question 4

Which number is divisible by 8?

A) 1638 B) 2648 C) 2564 D) 3126 Question 5

Which of the following numbers are divisible by 2, 5 and 10?

A. 19400 B. 125370 C. 3000000 D. 580911 Question 6 When 2 256 2256 is divided by 17 17

, what will be the remainder?

A) 1 1 B) 16 16 C) 14 14 D) None of these Question 7

Find the least five digit number which is divisible by 666.

(A) 10656 (B) 10646 (C) 10666 (D) 10626 Question 8

Which of the following numbers is divisible by 15?

A.30560 B.29515 C.23755 D.17325 Question 9

The remainder obtained when

1!+2!+......49! 1!+2!+......49! is divided by 20 20 is (a) 13 (a) 13 (b) 33 (b) 33 (c) 12 (c) 12 (d) 11 (d) 11

Guys, does anyone know the answer?