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.

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.

• 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.