Divisibility Rule of 2 with Examples

Divisibility rules are like tricks that help us determine whether one number can be divided by another without going through the actual division process. They simplify the process of checking if a number is divisible making it more convenient especially when working with larger numbers.

Divisibility Rule of 2 states that a number is divisible by 2 if it is even. An even number can always be expressed as twice another integer.

For example:

• 26 = 2 \times 13
• 28 = 2 \times 14
• 36 = 2 \times 18
• 100 = 2 \times 50

More Examples on Divisibility Rule of 2

• 130 is divisible by 2 because it ends in 0.
• 5406 is divisible by 2 because it ends in 6.
• 1231 is not divisible by 2 because it ends in 1.
• 1,293,023 is not divisible by 2 because it ends in 3.

This rule simplifies the process of checking divisibility by allowing us to quickly determine if a number is divisible by 2 based on its last digit.

Proof of Divisibility Rule of 2

Any number N can be expressed in the form of a sum of powers of 10. For example, the number 1234 can be written as:

N = 1⋅10³ + 2⋅10² + 3⋅10¹ + 4⋅10⁰

In general, for a number with digits d_n​, d_n-1,......d₁, d_0, the number can be written as:

N = d_n \cdot 10^n + d_{n-1} \cdot 10^{n-1} + \dots + d_1 \cdot 10^1 + d_0 \cdot 10^0

Now, Taking 10 common in the above expression,

N = 10 (d_n + d_n-1 . 10^n-2 + d_n-2 . 10^n-3 + .........) + d₀

In fact, for all n ≥ 1, 10ⁿ is divisible by 2.

Since all powers of 10 (except 10⁰) are divisible by 2, the only part of N that determines its divisibility by 2 is the last term, which is d₀. 10⁰ = d₀.

Thus, for the whole number N to be divisible by 2, the last digit d₀​ must be divisible by 2.

Verification with Table of 2

2 : Even
4 : Even
6 : Even
8 : Even
10 : 0 (Even)
12 : 2 (Even)
14 : 4 (Even
16 : 6 (Even)
18 : 8 (Even)
20 : 0 (Even)

Solved Examples on Divisibility Rule of 2

Example 1: Check if 268 is divisible by 2.

Solution:

Given, 288 is a number.

If the last digit of 268 is 8 which is divisible by 2, then 288 is also divisible by 2.

The last digit of 268 is 8, which is divisible by 2, such that;

8/2 = 4

Hence, 268 satisfies the divisibility of 2.

Example 2: Is 780 divisible by 2?

Solution:

Yes, 780 is divisible by 2 as the unit's place digit is 0.

Example 3: Which of the following integers is divisible by two, and why?

14 77 46 80 99 26 33 48

Solution:

14 is divisible by 2 as the last digit is an even number.

77 is not divisible by 2 as the last digit is an odd number.

46 is divisible by 2 as the digit in the unit’s place is 6.

80 is divisible by 2 as the last digit is zero.

99 is not divisible by 2 as the last digit is an odd number.

26 is divisible by 2 as the digit at the unit's place is an even.

33 is not divisible by 2 as the number ends with an odd number.

48 is divisible by 2 as the last digit is an even number.

Example 4: Test the divisibility of the following numbers by 2.

236, 254, 289, 278

Solution:

As per the divisibility rule of 2, a number is divisible by 2 if it is even or if the last digit is an even number, i.e., 2, 4, 6, 8 including 0.

So, let us apply this rule to all the given numbers.

a.) 236: Here, the last digit is 6 which is an even number. Therefore, 236 is divisible by 2.

b.) 254: Here, the last digit is 4 which is an even number. Therefore, 254 is divisible by 2.

c.) 289: Here, the last digit is 9 which is an odd number. Therefore, 289 is not divisible by 2.

d.) 278: Here, the last digit is 8 which is an even number. Therefore, 278 is divisible by 2.

Thus, out of the listed numbers, 236, 254, 289, and 278, only 289 is not divisible by 2. This means 236, 254, and 278 are divisible by 2.

Example 5: Check the divisibility of the following numbers by 9:

354, 765, 243, 405

Solution:

As per the divisibility rule of 9, the sum of all the digits of the number should be divisible by 9. So, let us apply this rule to all the given numbers:

a.) 354: Here, 3 + 5 + 4 = 12, but 12 is not divisible by 9. Therefore, 354 is not divisible by 9.

b.) 765: Here, 7 + 6 + 5 = 18 and 18 is divisible by 9. Therefore, 765 is divisible by 9.

c.) 243: Here, 2 + 4 + 3 = 9, and 9 is divisible by 9. Therefore, 243 is divisible by 9.

d.) 405: Here, 4 + 0 + 5 = 9 and 9 is divisible by 9. Therefore, 405 is divisible by 9.

Thus, out of the listed numbers, 354, 765, 243, and 405 only 354 is not divisible by 9. This means 765, 243, and 405 are divisible by 9.

Divisiblity Rule of 2 Worksheet

1. Is the number 146 divisible by 2?

2. Check if 3,582 is divisible by 2.

3. Determine whether the number 57,849 is divisible by 2.

4. Is the number 1,234,567 divisible by 2?

5. Find out if 90 is divisible by 2.

Also Read: Practice Questions on Divisibility Rules

Conclusion

The digits 0, 2, 4, 6 and 8 can be divided by 2. This means that numbers that are multiples of two and those ending with a zero are also divisible by two. We know that even numbers are essentially multiples of two. Therefore we can conclude that every even number is divisible by two. On the hand numbers like 1, 3, 5, 7 and 9 which have an digit cannot be divided by two.

Other Divisibility Rules:

• Divisibility by 3
• Divisibility by 5
• Divisibility by 4
• Divisibility by 6
• Divisibility by 9
• Divisibility by 8