198 LearnersLast updated on May 26th, 2025
Divisibility Rule of 107
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 107.
What is the Divisibility Rule of 107?
The divisibility rule for 107 is a method by which we can find out if a number is divisible by 107 or not without using the division method. Check whether 3210 is divisible by 107 with the divisibility rule.
Step 1: Break down the number into groups of three digits starting from the right. In 3210, the groups are 3 and 210.
Step 2: Subtract the first group from the second group. i.e., 210 - 3 = 207.
Step 3: As it is shown that 207 is not a multiple of 107, therefore, the number is not divisible by 107. If the result from step 2 is a multiple of 107, then the number is divisible by 107.
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Tips and Tricks for Divisibility Rule of 107
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 107.
- Know the multiples of 107: Memorize the multiples of 107 (107, 214, 321, 428… etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 107, then the number is divisible by 107.
- Use negative numbers: If the result we get after the subtraction is negative, we will avoid the symbol and consider it as positive for checking the 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 107. For example: Check if 21407 is divisible by 107 using the divisibility test. Break into groups: 21 and 407. Subtract the first group from the second group: 407 - 21 = 386. Still, 386 is a large number, so we will repeat the process again: 38 and 6, 38 - 6 = 32. Since 32 is not a multiple of 107, 21407 is not divisible by 107.
- 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 107
The divisibility rule of 107 helps us quickly check if a given number is divisible by 107, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, grouping digits into threes and then subtracting the first group from the second group to check if it is a multiple of 107.
Mistake 2
Not considering the group size.
Students should remember to break numbers into groups of three digits, starting from the right.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have a large number resulting from subtraction. The process should be repeated until we get the smallest number that is divisible by 107.
Mistake 4
Not considering the negative values.
Students should consider negative values as positive when checking for divisibility, as the rule applies to both positive and negative numbers.
Mistake 5
Confusing the steps.
Students often confuse the steps or forget them; to avoid this error, students should practice regularly.
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Divisibility Rule of 107 Examples
Problem 1
Is 2140 divisible by 107?
Yes, 2140 is divisible by 107.
Explanation
To check if 2140 is divisible by 107, follow these steps:
1) Double the last digit of the number, 0 × 2 = 0.
2) Subtract the result from the remaining digits, excluding the last digit, 214 – 0 = 214.
3) Since 214 is a multiple of 107 (107 × 2 = 214), 2140 is divisible by 107.
Problem 2
Check the divisibility rule of 107 for 5350.
Yes, 5350 is divisible by 107.
Explanation
To check if 5350 is divisible by 107:
1) Double the last digit, 0 × 2 = 0.
2) Subtract the result from the remaining digits, excluding the last digit, 535 – 0 = 535.
3) Since 535 is a multiple of 107 (107 × 5 = 535), 5350 is divisible by 107.
Problem 3
Is 1284 divisible by 107?
No, 1284 is not divisible by 107.
Explanation
To check the divisibility of 1284 by 107:
1) Double the last digit, 4 × 2 = 8.
2) Subtract the result from the remaining digits, excluding the last digit, 128 – 8 = 120.
3) Since 120 is not a multiple of 107, 1284 is not divisible by 107.
Problem 4
Can 962 be divisible by 107 following the divisibility rule?
No, 962 is not divisible by 107.
Explanation
To check if 962 is divisible by 107:
1) Double the last digit, 2 × 2 = 4.
2) Subtract the result from the remaining digits, excluding the last digit, 96 – 4 = 92.
3) Since 92 is not a multiple of 107, 962 is not divisible by 107
Problem 5
Check the divisibility rule of 107 for 321.
Yes, 321 is divisible by 107.
Explanation
To check if 321 is divisible by 107:
1) Double the last digit, 1 × 2 = 2.
2) Subtract the result from the remaining digits, excluding the last digit, 32 – 2 = 30.
3) Since 30 is not a multiple of 107, I made a mistake in my calculation. Let me correct this. Since my previous calculation was incorrect, let me retry: 321 should be checked directly using division as no simple divisibility trick applies here. Thus, 321 divided by 107 gives a whole number (3), confirming it is divisible by 107.
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FAQs on Divisibility Rule of 107
1. What is the divisibility rule for 107?
2.How many numbers are there between 1 and 1000 that are divisible by 107?
3.Is 214 divisible by 107?
4.What if I get 0 after subtraction?
5.Does the divisibility rule of 107 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 107?
7.What are some fun ways kids in United States can practice Divisibility Rule of 107 with numbers?
8.What role do numbers and Divisibility Rule of 107 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 107 skills?
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Important Glossaries for Divisibility Rule of 107
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 107 are 107, 214, 321, 428, etc.
- Subtraction: Subtraction is a process of finding out the difference between two numbers by reducing one number from another.
- Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.
- Grouping: Grouping involves organizing numbers into sets or groups, such as dividing a number into groups of three digits.
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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.
