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156 LearnersLast updated on February 16th, 2025
Divisibility Rule of 666
The divisibility rule is a way to determine 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 666.
What is the Divisibility Rule of 666?
The divisibility rule for 666 is a method by which we can find out if a number is divisible by 666 or not without using the division method. Check whether 1998 is divisible by 666 with the divisibility rule.
Step 1: Check the divisibility of the number by 2. Since 1998 ends in 8, which is even, it is divisible by 2.
Step 2: Check the divisibility by 3 by adding the digits. The sum of the digits of 1998 is 1 + 9 + 9 + 8 = 27, which is divisible by 3.
Step 3: Check the divisibility by 37. Divide 1998 by 37. Since 1998 ÷ 37 = 54, which is an integer, it is divisible by 37.
Since 1998 is divisible by 2, 3, and 37, it is divisible by 666 (since 666 = 2 × 3 × 37).
Tips and Tricks for Divisibility Rule of 666
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 666.
- Know the factors of 666: Memorize the factors of 666 (2, 3, 37) to quickly check the divisibility.
- Use the divisibility rules of individual factors: If a number is divisible by 2, 3, and 37, then it is divisible by 666.
- Repeat the process for large numbers: Students should keep repeating the divisibility process for each factor until they conclude whether the number is divisible by 666.
- 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 to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 666
The divisibility rule of 666 helps us quickly check if a given number is divisible by 666, 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 checking all factors.
Students should ensure they check divisibility by 2, 3, and 37.
Divisibility Rule of 666 Examples
Problem 1
Is 1998 divisible by 666?
Yes, 1998 is divisible by 666.
Explanation
To check the divisibility rule of 666 for 1998, we follow these steps:
1) Check if 1998 is divisible by 2, 3, and 37.
2) 1998 is even, so it is divisible by 2.
3) Sum of the digits: 1 + 9 + 9 + 8 = 27, which is divisible by 3.
4) Divide 1998 by 37: 1998 ÷ 37 = 54, which is a whole number.
Since 1998 is divisible by 2, 3, and 37, it is divisible by 666.
Problem 2
Is 2664 divisible by 666?
Yes, 2664 is divisible by 666.
Explanation
To determine if 2664 is divisible by 666, use these steps:
1) Check divisibility by 2, 3, and 37.
2) 2664 is even, hence divisible by 2.
3) Sum of the digits: 2 + 6 + 6 + 4 = 18, which is divisible by 3.
4) Divide 2664 by 37: 2664 ÷ 37 = 72, which is a whole number.
Since 2664 meets the criteria for divisibility by 2, 3, and 37, it is divisible by 666.
Problem 3
Is 1332 divisible by 666?
No, 1332 is not divisible by 666.
Explanation
To check the divisibility of 1332 by 666, consider the following:
1) Check divisibility by 2, 3, and 37.
2) 1332 is even, so it is divisible by 2.
3) Sum of the digits: 1 + 3 + 3 + 2 = 9, which is divisible by 3.
4) Divide 1332 by 37: 1332 ÷ 37 ≈ 36.0, which is a whole number.
Although 1332 is divisible by 2, 3, and 37 individually, it must also be divisible by all three together to be divisible by 666. However, since 1332 is actually divisible by all three, the mistake lies in our arithmetic check. 1332 ÷ 666 = 2, which is a whole number, indicating the original answer should be yes, 1332 is divisible by 666.
Problem 4
Is 732 divisible by 666?
No, 732 is not divisible by 666.
Explanation
To check divisibility of 732 by 666, proceed as follows:
1) Check divisibility by 2, 3, and 37.
2) 732 is even, so it is divisible by 2.
3) Sum of the digits: 7 + 3 + 2 = 12, which is divisible by 3.
4) Divide 732 by 37: 732 ÷ 37 ≈ 19.78, not a whole number.
Since 732 fails divisibility by 37, it is not divisible by 666.
Problem 5
Is 3996 divisible by 666?
Yes, 3996 is divisible by 666.
Explanation
To verify if 3996 is divisible by 666, check these conditions:
1) Check divisibility by 2, 3, and 37.
2) 3996 is even, hence divisible by 2.
3) Sum of the digits: 3 + 9 + 9 + 6 = 27, which is divisible by 3.
4) Divide 3996 by 37: 3996 ÷ 37 = 108, which is a whole number.
Given that 3996 is divisible by 2, 3, and 37, it is divisible by 666.
FAQs on Divisibility Rule of 666
1.What is the divisibility rule for 666?
2.How many numbers are there between 1 and 2000 that are divisible by 666?
3.Is 1332 divisible by 666?
4.What if I get a remainder after dividing by a factor?
5.Does the divisibility rule of 666 apply to all integers?
Important Glossaries for Divisibility Rule of 666
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Factors: Numbers that are multiplied together to get another number. For example, factors of 666 are 2, 3, and 37.
- Integers: Integers are numbers that include all the whole numbers, negative numbers, and zero.
- Divisibility: A condition where one integer can be divided by another without leaving a remainder.
- Verification: The process of checking or proving the correctness of a result.
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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.
