In this article we would like to study about the divisibility rule and solve Number System Divisibility Questions related to Number System. Number System is an important topic for Tet Exam. Factors, factorization, divisibility, divisibility rule, LCM, HCF etc. are the topics in number system. Today,
Divisibility Rule
Contents
Divisibility Rule in Number System
Divisibility by 2
The numbers which end with 0, 2, 4, 6, and 8 are divisible by 2. The numbers which are divisible by 2 are called even numbers.
Example 1000, 10098, 26354, etc.
Divisibility by 3
Any number whose sum of digits is divisible by 3 is divisible by 3.
Divisibility by 4
To check the divisibility of any number by 4, its last 2 digits are checked, if the last 2 digits are zeros or divisible by 4, then that number will be divisible by 4.
Divisibility by 5
To check the divisibility of any number by 5, its last digit is checked, if the last digit is zero or 5 then that number will be divisible by 5.
Divisibility by 6
To check the divisibility of a number by 6, the divisibility by 2 and 3 has to be checked. If a number is divisible by 2 and 3, then that number is also divisible by 6. That is, if a number is even and the sum of its digits is divisible by 3, then that number is divisible by 6.
Divisibility by 7
Check the divisibility of a number by 7 follow the following procedure
Step-1
double its last digit i.e. the unit digit.
Step-2
subtract it from the remaining number.
Step-3
If the obtained number is either 0 or divisible by 7 then the given number will be divisible by 7.
Step-4
If the obtained number is again a large number, then repeat all the steps again by doubling the unit digit of that obtained number and repeat all these steps until you get 0 or a number that can be easily divided by 7.
Example
to check whether 284 is divisible by 7 or not follow, the procedure given above as follows
Step-1
4×2=8
Step-2
28-8=20
Step-3
20 is not divisible by 7 therefore 284 is also not divisible by 7.
Divisibility by 8
If you want to check the divisibility of a number by 8, then simply check the last three digits of that number. If the last three digits are divisible by 8, then the number is also divisible by 8.
Divisibility by 9
The divisibility rule of 9 will be similar to the divisibility rule of 3 i.e. if the sum of the digits of a number is divisible by 9 then that number will also be divisible by 9.
Divisibility by 11
If you want to check the divisibility of a number by 11 then follow the following procedure
Step-1
sum the digits of the even place.
Step-2
sum the digits of the odd place.
Step-3
subtract both.
Step-4
If the number obtained is either 0 or divisible by 11, then that number will also be divisible by 11.
Example
to check whether 28435453 is divisible by 11 or not follow, the procedure given above as follows
Step-1
8+3+4+3=18
Step-2
2+4+5+5=16
Step-3
18-16=2
2 is not divisible by 11 therefore 28435453 is also not divisible by 11.
Divisibility by 13
The divisibility rule of 13 is similar to the divisibility rule of 7 but with a few changes. Multiply the last digit of a number by 9 and subtract it from the rest of the number. If the number obtained is 0 or divisible by 13, then the given number is divisible by 13.
Divisibility by 17
The divisibility rule of 17 is the same as that of 7 but in this, the last digit is multiplied by 5 instead of 2. If you want to know whether the given number is divisible by 17 or not then multiply the last digit by 5 and subtract it from the remaining number if the number obtained is 0 or divisible by 17 then the given number will be divisible by 17.
Check the divisibility of a number by 17 follow the following procedure
Step-1
Multiply last digit by 5.
Step-2
subtract it from the remaining number.
Step-3
If the obtained number is either 0 or divisible by 17 then the given number will be divisible by 17.
Step-4
If the obtained number is again a large number, then repeat all the steps again by doubling the unit digit of that obtained number and repeat all these steps until you get 0 or a number that can be easily divided by 17.
Example
to check whether 2845 is divisible by or not follow, the procedure given above as follows
Step-1
5×5=25
Step-2
284-25=259
259 is the larger number then again apply step-1 on 259.
9×5=45
25-45=20
Step-3
20 is not divisible by 7 therefore 284 is also not divisible by 7.
Number System Divisibility Questions Answer
Q1- What is the product of the greatest number of 7 digits and the smallest number of 6 digits?
i) 999999900000
ii) 9999999000
iii) 9999999000000
iv) 99999990000
i)999999900000
Q2- If 775 dollars is equal to 63,550 then how many dollars are equivalent to 820?
i)12
ii)15
iii)10
iv)11
iii)10
Q3- 128 is not divisible by which of the following numbers?
i) 4
ii) 8
iii) 6
iv) 2
iii)6
Q4- What will you get when the smallest 2-digit number is subtracted from the largest 3-digit number?
i) 9990
ii) 890
iii) 989
iv) 89
iii)989
Q5- How many numbers between 20 and 120 are divisible by 7?
i) 15
ii) 16
iii) 14
iv) 18
i)15
Q6- Which of the following numbers is divisible by 7?
i) 9059
ii) 9057
iii) 9061
iv) 9051
iv)9051
Q7- The number “112112x” is divisible by 11 then finds the value of x?
i) 1
ii) 2
iii) 3
iv) 0
iv)0
Q8- Which of the following numbers is divisible by 11?
i) 158959
ii) 158280
iii) 158158
iv) 158258
iii)158158
Q9- Which of the following numbers is divisible by both 4 and 6 ?
i) 11,994
ii) 12,006
iii) 12012
iv) None of these
iii)12012
Q10- Which of the following numbers are divisible by all the numbers 2, 3, 4, 6, and 8?
i) 14,576
ii) 16,576
iii) 15,576
iv) 15,586
iii)15,576
Q11- The number “269×56” is divisible by 6 .finds the value of x?
i) 0
ii)2
iii) 1
iv) 3
ii)2
Q12- A Shopkeeper bought 10 tonnes of wheat and sold 7.76 tonnes of wheat, how many kg of wheat was left with him?
i) 224kg
ii) 2240kg
iii) 22kg
i ) 726kg
ii)2240
Q13-225 meter wire is cut into 50 equal parts, what will be the length of each part?
i) 5 meter
ii) 450 cm
iii) 5.5 meter
iv) 550 cm
ii)450cm
Q14- Which of the following numbers is divisible by 9 in Number System?
i) 73736
ii) 737373
iii) 73737
iv) 73736
iii)73737
Q15- Which of the following is the correct statement?
i) No even number can be a prime number.
ii) 2 is the smallest prime number.
iii) 3 is the smallest prime number.
iv) 2 is a composite number as well as a prime number.
ii) 2 is the smallest prime number.
Q16. What will be the remainder when 12578951 is divided by 11?
i)1
ii)2
iii)4
iv)0
iv)0
Q17. Find the number of prime numbers between 50 and 100?
i) 15
ii)11
iii)13
iv)10
iv)10
Q18. A number divided by 89 gives 155 as the quotient and 47 as the remainder. Find that number?
i)16075
ii)13842
iii)16842
iv)13075
ii)13842
Q19. Check which of the following number is divisible by 13?
i) 2276
ii) 4871
iii) 6179
iv) 3575
iv)3575
Q20. Which of the following number is divisible by 17?
i)5226
ii)14,154
iii)19,125
iv)2756
iii)19,125
FAQs on Number System Divisibility Questions
Q. What are the 7 types of numbers?
ANSWER: In number system their are Real number, Complex number, Natural number, Whole number, Integers, Rational number, and Irrational number
Q. Is Pi a real number?
ANSWER: Yes, Pi is a real and irrational number.
Q. Is negative a real number?
ANSWER: Yes, A real number can be positive or negative.