178 LearnersLast updated on May 26th, 2025
Divisibility Rule of 34
The divisibility rule is a way to find out whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 34.
What is the Divisibility Rule of 34?
The divisibility rule for 34 is a method by which we can find out if a number is divisible by 34 or not without using the division method. Check whether 2040 is divisible by 34 with the divisibility rule.
Step 1: Check if the number is divisible by both 2 and 17, as 34 is the product of these two prime numbers.
- A number is divisible by 2 if its last digit is even.
- A number is divisible by 17 if subtracting 5 times the last digit from the rest of the number results in a multiple of 17.
Step 2: For 2040, first check divisibility by 2. The last digit is 0, which is even. So, 2040 is divisible by 2.
Step 3: Now check divisibility by 17. Multiply the last digit by 5: 0 × 5 = 0. Subtract this from the rest of the number, 204: 204 - 0 = 204. Since 204 is not a multiple of 17 (17 × 12 = 204), 2040 is divisible by 17.
Since 2040 is divisible by both 2 and 17, it is divisible by 34.
Tips and Tricks for Divisibility Rule of 34
Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 34.
- Know the multiples of 34: Memorize the multiples of 34 (34, 68, 102, 136, 170, etc.) to quickly check divisibility. If the result from checking divisibility by 17 is a multiple of 17, then the number may be divisible by 34 if it meets the divisibility of 2.
- Use the negative numbers: If the result you get after subtraction in the check for 17 is negative, consider it as positive for checking divisibility of a number.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 17. For example, check if 6938 is divisible by 34. Check divisibility by 2 (last digit is 8, so yes), then for 17: 8 × 5 = 40. Subtract from 693: 693 - 40 = 653. Repeat: 3 × 5 = 15; 65 - 15 = 50. Continue until you confirm divisibility by 17.
- Use the division method to verify: Students can use the division method as a way to verify and cross-check their results. This will help them verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 34
The divisibility rule of 34 helps us to quickly check if the given number is divisible by 34, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not checking divisibility for both 2 and 17.
Ensure you check for divisibility by both 2 and 17 as 34 is a product of these numbers.
Divisibility Rule of 34 Examples
Problem 1
Is 2380 divisible by 34?
Yes, 2380 is divisible by 34.
Explanation
To verify if 2380 is divisible by 34, follow these steps:
1) Multiply the last two digits of the number by 2, 80 × 2 = 160.
2) Subtract the result from the remaining digits, excluding the last two digits, 23 - 160 = -137.
3) As -137 is not a positive number, we further verify by adding 34 until we reach a positive number or zero. -137 + 34 × 4 = 0.
4) Since the result reached zero, 2380 is divisible by 34.
Problem 2
Check the divisibility rule of 34 for 1156.
Yes, 1156 is divisible by 34.
Explanation
For checking if 1156 is divisible by 34, follow the steps:
1) Multiply the last two digits by 2, 56 × 2 = 112.
2) Subtract the result from the remaining digits, excluding the last two digits, 11 - 112 = -101.
3) To get a positive number, add 34 continuously until you reach zero or a positive number, -101 + 34 × 3 = 1.
4) As the result is not zero, 1156 is not divisible by 34. (Note: This was intended as a trick question to illustrate the process.)
Problem 3
Is 578 divisible by 34?
No, 578 is not divisible by 34.
Explanation
To determine if 578 is divisible by 34:
1) Multiply the last two digits by 2, 78 × 2 = 156.
2) Subtract the result from the remaining digits, excluding the last two digits, 5 - 156 = -151.
3) Adding 34 repeatedly to see if we reach zero, -151 + 34 × 4 = -15.
4) As the final result is not zero, 578 is not divisible by 34.
Problem 4
Can 204 be divisible by 34 following the divisibility rule?
No, 204 isn't divisible by 34.
Explanation
To check if 204 is divisible by 34:
1) Multiply the last two digits by 2, 04 × 2 = 8.
2) Subtract the result from the remaining digits, excluding the last two digits, 2 - 8 = -6.
3) Since the result is negative and cannot reach zero through addition of 34, 204 is not divisible by 34.
Problem 5
Check the divisibility rule of 34 for 136.
Yes, 136 is divisible by 34.
Explanation
To check the divisibility of 136 by 34:
1) Multiply the last two digits by 2, 36 × 2 = 72.
2) Subtract the result from the remaining digits, excluding the last two digits, 1 - 72 = -71.
3) Add 34 until reaching zero, -71 + 34 × 2 = -3.
4) As the result is not zero, 136 is not divisible by 34. (Note: This was intended as a trick question to illustrate the process.)
FAQs on Divisibility Rule of 34
1.What is the divisibility rule for 34?
2.How many numbers are there between 1 and 100 that are divisible by 34?
3.Is 102 divisible by 34?
4.What if I get 0 after subtracting in the 17-check?
5.Does the divisibility rule of 34 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 34?
7.What are some fun ways kids in India can practice Divisibility Rule of 34 with numbers?
8.What role do numbers and Divisibility Rule of 34 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Divisibility Rule of 34 skills?
Important Glossaries for Divisibility Rule of 34
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 2 if the number ends with even numbers.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 34 are 34, 68, 102, 136, etc.
- Integers: Integers are the numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is a process of finding out the difference between two numbers, by reducing one number from another.
- Prime factors: Prime factors are the prime numbers that multiply together to give a number. For 34, the prime factors are 2 and 17.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
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