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124 LearnersLast updated on February 18th, 2025
Divisibility Rule of 930
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 930.
What is the Divisibility Rule of 930?
The divisibility rule for 930 is a method by which we can find out if a number is divisible by 930 or not without using the division method. Check whether 1860 is divisible by 930 with the divisibility rule.
Step 1: Check if the number is divisible by both 10 and 93. First, ensure that the last digit is 0, which confirms divisibility by 10.
Step 2: For divisibility by 93, sum the digits of the number and check if the result is divisible by 3 (since 93 is divisible by 3) and also verify if the number itself is divisible by 31 (since 93 is 3×31).
Step 3: If both conditions are met, the number is divisible by 930. If not, the number isn't divisible by 930.
Tips and Tricks for Divisibility Rule of 930
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 930.
Know the factors of 930:
Memorize that 930 is 10×93, and 93 is 3×31. This helps in quickly checking the divisibility by its factors.
Use known divisibility rules:
Use the divisibility rules for 10, 3, and 31 to simplify the process.
Repeat the process for large numbers:
Students should keep repeating the divisibility process for each factor of 930 until they reach a final conclusion.
Use the division method to verify:
Students can use the division method as a way to verify and crosscheck their results. This helps them verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 930
The divisibility rule of 930 helps us quickly check if a given number is divisible by 930, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes that will help you.
Mistake 1
Not checking divisibility by all factors.
Students should ensure the number is divisible by 10, 3, and 31, as 930 is a product of these numbers.
Divisibility Rule of 930 Examples
Problem 1
Is 4650 divisible by 930?
Yes, 4650 is divisible by 930.
Explanation
To check if 4650 is divisible by 930, we simplify using prime factors.
1) The prime factors of 930 are 2, 3, 5, and 31.
2) Check if 4650 is divisible by these factors:
- 4650 is even, so it's divisible by 2.
- The sum of digits, 4 + 6 + 5 + 0 = 15, is divisible by 3.
- The last digit is 0, so it's divisible by 5.
- 4650 divided by 31 gives an integer, 150, so it's divisible by 31.
Since 4650 is divisible by all prime factors of 930, it is divisible by 930.
Problem 2
Check the divisibility rule of 930 for 7440.
No, 7440 is not divisible by 930.
Explanation
To check if 7440 is divisible by 930, we will verify divisibility by the prime factors of 930.
1) The prime factors of 930 are 2, 3, 5, and 31.
2) Check if 7440 is divisible by these factors:
- 7440 is even, so it's divisible by 2.
- The sum of digits, 7 + 4 + 4 + 0 = 15, is divisible by 3.
- The last digit is 0, so it's divisible by 5.
- 7440 divided by 31 does not yield an integer.
Since 7440 is not divisible by 31, it is not divisible by 930.
Problem 3
Is -2790 divisible by 930?
Yes, -2790 is divisible by 930.
Explanation
To check if -2790 is divisible by 930, we ignore the negative sign and check divisibility.
1) The prime factors of 930 are 2, 3, 5, and 31.
2) Check if 2790 is divisible by these factors:
- 2790 is even, so it's divisible by 2.
- The sum of digits, 2 + 7 + 9 + 0 = 18, is divisible by 3.
- The last digit is 0, so it's divisible by 5.
- 2790 divided by 31 gives an integer, 90, so it's divisible by 31.
Since 2790 is divisible by all prime factors of 930, it is divisible by 930.
Problem 4
Can 3720 be divisible by 930 following the divisibility rule?
No, 3720 isn't divisible by 930.
Explanation
To check if 3720 is divisible by 930, we look at its prime factors.
1) The prime factors of 930 are 2, 3, 5, and 31.
2) Check if 3720 is divisible by these factors:
- 3720 is even, so it's divisible by 2.
- The sum of digits, 3 + 7 + 2 + 0 = 12, is divisible by 3.
- The last digit is 0, so it's divisible by 5.
- 3720 divided by 31 does not yield an integer.
Since 3720 is not divisible by 31, it is not divisible by 930.
Problem 5
Check the divisibility rule of 930 for 1860.
No, 1860 is not divisible by 930.
Explanation
To check the divisibility of 1860 by 930, we examine its prime factors.
1) The prime factors of 930 are 2, 3, 5, and 31.
2) Check if 1860 is divisible by these factors:
- 1860 is even, so it's divisible by 2.
- The sum of digits, 1 + 8 + 6 + 0 = 15, is divisible by 3.
- The last digit is 0, so it's divisible by 5.
- 1860 divided by 31 does not yield an integer.
Since 1860 is not divisible by 31, it is not divisible by 930.
FAQs on Divisibility Rule of 930
1.What is the divisibility rule for 930?
2.How many numbers are there between 1 and 18600 that are divisible by 930?
3.Is 1860 divisible by 930?
4.What if the sum of the digits is divisible by 3 but not the number itself?
5.Does the divisibility rule of 930 apply to all integers
Important Glossaries for Divisibility Rule of 930
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Factors: Numbers that evenly divide another number. For 930, the factors include 10, 3, and 31.
- Multiples: Numbers that are the product of a number and an integer. For example, multiples of 930 are 930, 1860, etc.
- Sum of digits: The total obtained by adding all the digits in a number. Used in divisibility tests for 3.
- Integer: Whole numbers that can be positive, negative, or zero.
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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.
