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172 LearnersLast updated on February 24th, 2025
Divisibility Rule of 35
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 35.
What is the Divisibility Rule of 35?
The divisibility rule for 35 is a method by which we can find out if a number is divisible by 35 or not without using the division method. Check whether 2450 is divisible by 35 with the divisibility rule.
Step 1: Check the divisibility of the number by 5. The number should end in 0 or 5. Here, 2450 ends in 0.
Step 2: Check the divisibility of the number by 7. Use the rule for 7: double the last digit and subtract from the rest. For 245, double 0 is 0, and 245−0=245. Double 5 is 10, and 24−10=14, which is a multiple of 7.
Step 3: Since 2450 is divisible by both 5 and 7, it is divisible by 35.
Tips and Tricks for Divisibility Rule of 35
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 35.
- Know the multiples of 35: Memorize the multiples of 35 (35, 70, 105, 140, 175, etc.) to quickly check divisibility. If both divisibility rules for 5 and 7 are satisfied, then the number is divisible by 35.
- Use the divisibility rules for 5 and 7: Combining these rules helps verify divisibility by 35. If a number is divisible by both 5 and 7, it’s divisible by 35.
- Repeat the process for large numbers: For larger numbers, verify divisibility by 5 and 7 separately and ensure both conditions are met.
- 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 35
The divisibility rule of 35 helps us quickly check if a number is divisible by 35, but common mistakes like calculation errors lead to incorrect conclusions. Here are some common mistakes and solutions.
Mistake 1
Not checking divisibility by both 5 and 7.
Ensure that the number satisfies the divisibility conditions for both 5 and 7.
Divisibility Rule of 35 Examples
Problem 1
Is the number of pages in a book, 245, divisible by 35?
Yes, 245 is divisible by 35.
Explanation
To check the divisibility by 35, verify divisibility by both 5 and 7.
1) For divisibility by 5, the last digit is 5, so 245 is divisible by 5.
2) For divisibility by 7, multiply the last digit by 2, 5 × 2 = 10.
3) Subtract the result from the remaining digits, 24 – 10 = 14.
4) Check if 14 is a multiple of 7, yes, 14 is a multiple of 7 (7 × 2 = 14).
Since 245 is divisible by both 5 and 7, it is divisible by 35.
Problem 2
A factory produces 560 units. Is this number divisible by 35?
Yes, 560 is divisible by 35.
Explanation
Check divisibility by both 5 and 7.
1) For divisibility by 5, the last digit is 0, so 560 is divisible by 5.
2) For divisibility by 7, multiply the last digit by 2, 0 × 2 = 0.
3) Subtract the result from the remaining digits, 56 – 0 = 56.
4) Check if 56 is a multiple of 7, yes, 56 is a multiple of 7 (7 × 8 = 56).
Since 560 is divisible by both 5 and 7, it is divisible by 35.
Problem 3
Is the number 315, representing the total score in a game, divisible by 35?
Yes, 315 is divisible by 35.
Explanation
Verify divisibility by both 5 and 7.
1) For divisibility by 5, the last digit is 5, so 315 is divisible by 5.
2) For divisibility by 7, multiply the last digit by 2, 5 × 2 = 10.
3) Subtract the result from the remaining digits, 31 – 10 = 21.
4) Check if 21 is a multiple of 7, yes, 21 is a multiple of 7 (7 × 3 = 21).
Since 315 is divisible by both 5 and 7, it is divisible by 35.
Problem 4
A shipment contains 490 items. Is this number divisible by 35?
Yes, 490 is divisible by 35.
Explanation
Check divisibility by both 5 and 7.
1) For divisibility by 5, the last digit is 0, so 490 is divisible by 5.
2) For divisibility by 7, multiply the last digit by 2, 0 × 2 = 0.
3) Subtract the result from the remaining digits, 49 – 0 = 49.
4) Check if 49 is a multiple of 7, yes, 49 is a multiple of 7 (7 × 7 = 49).
Since 490 is divisible by both 5 and 7, it is divisible by 35.
Problem 5
Is the number 672, representing the total attendance at an event, divisible by 35?
No, 672 is not divisible by 35.
Explanation
Check divisibility by both 5 and 7.
1) For divisibility by 5, the last digit is 2, so 672 is not divisible by 5.
2) Because 672 is not divisible by 5, it cannot be divisible by 35, regardless of its divisibility by 7.
FAQs on Divisibility Rule of 35
1.What is the divisibility rule for 35?
2.How many numbers are there between 1 and 100 that are divisible by 35?
3.Is 245 divisible by 35?
4.What if a number is divisible by 5 but not by 7?
5.Does the divisibility rule of 35 apply to all integers?
Important Glossaries for Divisibility Rule of 35
- 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 5 if it ends in 0 or 5.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 35 are 35, 70, 105, 140, etc.
- Integer: Integers are numbers that include all the 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.
- Verification: The process of confirming whether a calculated result is accurate or not, using methods such as division.
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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.
Fun Fact
: She loves to read number jokes and games.
