Arithmetic aptitude :: Numbers :: General Questions

• Numbers - General Questions
• Numbers - Important Formulas and Facts

Divisibility Rule

A positive integer N is Divisible by,

2: if the last digit of N is 2, 4, 6, 8, or 0;
3: if the sum of digits of N is a multiple of 3;
4: if the last 2 digits of N are a multiple of 4;
5: if the last digit of N is either 0 or 5;
6: if N is divisible by both 2 and 3;
7: if subtracting twice the last digit of N from the remaining digits gives a multiple of 7
(e.g 658 = 65 - 2 x 8 = 65 - 16 = 49, which is a multiple of 7)
8: if the last 3 digits of N are a multiple of 8;
9: if the sum of digits of N is a multiple of 9;
10: if the last digit of N is 0;
11: if the difference of the alternating sum of digits of N is a multiple of 11
(e.g. 510510 = (5 + 0 + 1) - (1 + 5 + 0) = 6 - 6 = 0, So this is divisible by 11)
12: if N is divisible by both 3 and 4.

For more informations about Divisibility rules, please check, Wikipedia

Unit Digit

Unity means one, so the units digit is the digit in the one's column.
(e.g for the number 168, 8 is the unit digit)

To find out the unit digit in the product of the numbers, only consider the unit digit in each numbers

e.g. 753 x 43 x 1236 x 864

unit digit in each numbers

3 x 3 x 6 x 4 = 216, So 6 is the unit digit.

A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232 etc. Any number of this form is exactly divisible by :

Answer:

Explanation:

Let the units digit be x and ten's digit be y

Number = 1000y + 100x + 10y + x = 1010y + 101x = 101(10y+x)

So this number is divisible by 101. Which is the smallest three-digit prime number.

The number 311311311311311311311 is :

Answer:

Explanation:

Sum of digits= 35 and so it is not divisible by 3.

(Sum of digits at odd places)- (Sum of digits at even places)= 19-16=3, not divisible by 11.

So, the given number is neither divided by 3 nor by 11.

Which of the following numbers is exactly divisible by all prime numbers between 1 and 17 ?

Answer:

Explanation:

The prime numbers between 1 and 17 are 2, 3, 5, 7, 11, 13

According to Divisibility rule for 2 : If the last digit of a number is 2, 4, 6, 8 or 0 that number is divisible by 2

So we can consider 440440 and 510510.

Then apply the Divisibility rule for 3, that is,  add the each digit in the number 

440440 : 4 + 4 + 0 + 4 + 4 + 0 = 16, which is not divisible by 3

510510 : 5 + 1 + 0 + 5 + 1 + 0 = 12, which is divisible by 3

So our answer should be  510510 . You can apply divisibility rule for 5, 7, 11, 13 to this number to check this satisfies all the conditions.

The value of P, when 4864 x 9P2 is divisible by 12

Answer:

Explanation:

Clearly, 4864 is divisible by 4.
So, 9P2 must be divisible by 3.
So, (9 + P + 2) must be divisible by 3.
P = 1.

Which of the following numbers is divisible by 3, 7, 9 and 11 ?

Answer:

Explanation:

639 is not divisible by 7

2079 is divisible by each of 3, 7, 9, 11.

• Numbers - General Questions