A number is divisible by if the units digit is even - that is, it divides by without a remainder.
Divisibility Rules for 2, 4, and 10 Practice Problems
Master divisibility tests with step-by-step practice problems. Learn to identify numbers divisible by 2, 4, and 10 using simple tricks and patterns.
📚Practice Divisibility Rules and Build Your Math Confidence
- Apply the even units digit rule to test divisibility by 2
- Use the last two digits method to check divisibility by 4
- Master the quick trick of multiplying tens digit by 2 for divisibility by 4
- Identify numbers ending in 0 as divisible by 10
- Solve real-world problems using multiple divisibility rules together
- Build speed and accuracy with mixed practice problems
Understanding Divisibility Rules for 2, 4 and 10
Complete explanation with examples
Divisibility Rules for 2, 4, and 10
Divisibility Criteria for 2
Divisibility Rules for 4
First way: A number is divisible by if its last two digits are divisible by .
Second way: Multiply the tens digit by and add the units digit. If the result obtained is a multiple of , then the original number is as well.
Divisibility Rules for 10
A number is divisible by if its units digit is .
Practice Divisibility Rules for 2, 4 and 10
Test your knowledge with 18 quizzes
If a number is divisible by 10, is it also therefore divisible by 2?
Examples with solutions for Divisibility Rules for 2, 4 and 10
Step-by-step solutions included
Exercise #1
Is the number 61 divisible by 10?
Step-by-Step Solution
To determine if 61 is divisible by 10, we use the divisibility rule for 10:
- A number is divisible by 10 if and only if its last digit is 0.
Let's apply this rule to the number 61:
- The last digit of 61 is 1.
- Since 1 is not 0, 61 does not satisfy the divisibility rule for 10.
Therefore, we conclude that 61 is not divisible by 10.
Hence, the correct answer is: No.
Answer:
No
Video Solution
Exercise #2
Is the number 30 divisible by 10?
Step-by-Step Solution
To determine whether the number 30 is divisible by 10, we will apply the divisibility rule for 10.
According to this rule, a number is divisible by 10 if its last digit is 0. Let's check the number 30:
- Step 1: Examine the last digit of 30.
The last digit of 30 is 0. - Step 2: Apply the divisibility rule:
Since the last digit is 0, 30 is divisible by 10.
Therefore, the conclusion is that 30 is divisible by 10. The correct answer is Yes, which corresponds to choice 1 in the provided options.
Answer:
Yes
Video Solution
Exercise #3
Is the number 60 divisible by 10?
Step-by-Step Solution
To determine if the number 60 is divisible by 10, we will apply the divisibility rule for 10:
- Step 1: Identify the last digit of the number 60. The last digit is 0.
- Step 2: Apply the divisibility rule: A number is divisible by 10 if its last digit is 0.
Since the last digit of 60 is 0, we conclude that 60 is divisible by 10.
Therefore, the answer to the question is Yes.
Answer:
Yes
Video Solution
Exercise #4
Is the number 15 divisible by 2?
Step-by-Step Solution
To determine if the number 15 is divisible by 2, we will apply the rule for divisibility by 2:
- A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.
Now, let's follow these steps:
Step 1: Identify the last digit of the number 15. The last digit is 5.
Step 2: Compare this digit with the criteria for divisibility by 2. The digit 5 is not in the set of digits {0, 2, 4, 6, 8}.
Since the last digit of 15 is not one of the digits that makes a number divisible by 2, 15 is not divisible by 2.
Therefore, the conclusion is clear: the number 15 is not divisible by 2.
Answer:
No
Video Solution
Exercise #5
Is the number 8 divisible by 2?
Step-by-Step Solution
To solve this problem, we'll follow these steps:
- Step 1: Identify if 8 is an even number.
- Step 2: Apply the divisibility rule for 2.
- Step 3: Determine if there is any remainder when dividing 8 by 2.
Now, let's work through each step:
Step 1: Observe that the number 8 is an even number because it ends in 8. Even numbers are defined as those ending in 0, 2, 4, 6, or 8.
Step 2: According to the divisibility rule for 2, any even number is divisible by 2. Thus, 8 is divisible by 2.
Step 3: To further verify, perform the division: with a remainder of 0, confirming that 8 is indeed divisible by 2.
Therefore, the solution to the problem is Yes, and the correct answer is the choice having "Yes".
Answer:
Yes
Video Solution
Frequently Asked Questions
How do you check if a number is divisible by 2?
+A number is divisible by 2 if its units digit (last digit) is even - that means 0, 2, 4, 6, or 8. For example, 48 is divisible by 2 because it ends in 8, while 677 is not because it ends in 7.
What are the two methods to test divisibility by 4?
+Method 1: Check if the last two digits are divisible by 4 (like 32 in 832). Method 2: Multiply the tens digit by 2 and add the units digit - if the result is divisible by 4, so is the original number.
Why does the divisibility rule for 10 only look at the last digit?
+Numbers divisible by 10 must be multiples of 10, which always end in 0. This is because 10 = 2 × 5, so any multiple of 10 will have both 2 and 5 as factors, resulting in a units digit of 0.
Can a number be divisible by 2, 4, and 10 at the same time?
+Yes! Numbers like 120, 240, and 80 are divisible by all three. These numbers must end in 0 (for 10), have even last digits (for 2), and their last two digits must be divisible by 4.
What's the fastest way to check divisibility by 4 for large numbers?
+Use the last two digits method. Instead of dividing the entire number, just look at the last two digits. If those digits form a number divisible by 4, then the whole number is divisible by 4. For example, in 56712, just check if 12 is divisible by 4.
Do divisibility rules work for negative numbers too?
+Yes, divisibility rules work the same way for negative numbers. The sign doesn't affect divisibility - focus only on the digits. For example, -48 is divisible by 2, 4, and 10 just like 48 is.
How can I remember all the divisibility rules?
+Create simple memory tricks: 'Even ends for 2', 'Last two for 4', and 'Zero ends for 10'. Practice with everyday numbers like phone numbers, addresses, or prices to make the rules automatic.
Are there any numbers that aren't divisible by 2, 4, or 10?
+Yes, many numbers aren't divisible by any of these. Odd numbers (ending in 1, 3, 5, 7, 9) aren't divisible by 2, 4, or 10. Examples include 13, 57, 89, and 135.