Divisibility Tests by 8 and 12

We will discuss here about the rules of divisibility tests by 8 and 12 with the help of different types of problems.

1. If ‘a’ is a positive perfect square integer, then a(a - 1) is always divisible by 

(a) 12

(b) multiple of 12

(c) 12 - x

(d) 24


‘a’ is a positive perfect square integer.

Let, a = x2

Now, a (a – 1) = x2(x2 – 1)

Therefore, a(a – 1) is always divisible by 12

Answer: (a)

Note: x2(x2 – 1) is always divisible by 12 for any positive integral values of x.


2. If m and n are two digits of the number 653mn such that this number is divisible by 80, then (m + n) is equal to

(a) 2

(b) 3

(c) 4

(d) 6


653xy is divisible by 80

Therefore, the values of y must be 0.

Now, 53x must be divisible by 8.

Therefore, the value of x = 6

Thus, the required sum of (x + y) = (6 + 0) = 6

Answer: (d)

Note: The number formed by last three digits when divisible by 8, then the number is divisible by 8.


3. The sum of first 45 natural numbers will be divisible by

(a) 21

(b) 23

(c) 44

(d) 46


Number of natural numbers (n) is 45

Therefore, Sum of numbers divisible by 45 and 46 ÷ 2 = 23

Therefore, according to the given options the required number is 23.

Answer: (b)

Note: Sum of ‘n’ terms of natural numbers is always divisible by {n or n/2 or (n + 1) or (n + 1)/2} and also by the factors of n or (n + 1)


4. How many digits from the unit’s digit must be divisible by 32, to make the complete number is divisible by 32?

(a) 2

(b) 4

(c) 5

(d) None of these


32 = 25

Therefore, required number of digits is 5

Answer: (c)

Note: Power of ‘2’ and ‘5’ indicate the number of digits from the unit’s digit to decide whether the number is divisible by what number.


5. If 4a3 + 984 = 13b7, which is divisible by 11, then find the value of (a + b)

(a) 8

(b) 9

(c) 10

(d) 11


13b7 is divisible by 11

Therefore, (3 + 7) – (1 + b) = 0

Or, 10 – 1 + b = 0

Therefore, b = 9

Now, 4a3 + 984 = 1397

Thus, a = 9 – 8 = 1

Therefore, required values of (a + b) = (1 + 9) = 10

Answer: (c)

Math Employment Test Samples

From Divisibility Tests by 8 and 12 to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

Recent Articles

  1. Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

    Mar 02, 24 05:31 PM

    The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

    Read More

  2. Subtraction of Fractions having the Same Denominator | Like Fractions

    Mar 02, 24 04:36 PM

    Subtraction of Fractions having the Same Denominator
    To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numera…

    Read More

  3. Addition of Like Fractions | Examples | Worksheet | Answer | Fractions

    Mar 02, 24 03:32 PM

    Adding Like Fractions
    To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com…

    Read More

  4. Comparison of Unlike Fractions | Compare Unlike Fractions | Examples

    Mar 01, 24 01:42 PM

    Comparison of Unlike Fractions
    In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a nu…

    Read More

  5. Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

    Feb 29, 24 05:12 PM

    Equivalent Fractions
    The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…

    Read More