Divisibility Rule of 309

The divisibility rule for 309 is a method by which we can find out if a number is divisible by 309 or not without using the division method. Check whether 61782 is divisible by 309 with the divisibility rule.  

Step 1: Break down 309 into its prime factors, which are 3, 3, and 103.

Step 2: Check if the number is divisible by 3. Add up the digits of 61782: 6 + 1 + 7 + 8 + 2 = 24. Since 24 is divisible by 3, 61782 is divisible by 3.

Step 3: Check if the number is divisible by 103. Use the division method to check if 61782 is divisible by 103. After performing the division, we find that 61782 is divisible by 103 without a remainder.

Step 4: Since 61782 is divisible by all the prime factors of 309, it is divisible by 309.

Learning divisibility rules helps kids master division. Let’s learn a few tips and tricks for the divisibility rule of 309.

1. Know the multiples of 309:

Memorize the multiples of 309 (309, 618, 927, etc.) to quickly check divisibility. If the number is a multiple of 309, then it is divisible by 309.

2. Use the breakdown of factors:

Break down 309 into its prime factors (3 and 103) and check divisibility with each factor separately.

3. Repeat the process for large numbers:

Students should keep repeating the divisibility process with the factors until they reach a small number that is divisible by all the factors. For example, check if 927 is divisible by 309 using the divisibility test. First, check divisibility by 3: 9 + 2 + 7 = 18, which is divisible by 3. Then use the division method for 103: 927 ÷ 103 = 9. Since 927 is divisible by both 3 and 103, it is divisible by 309.

4. 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: A set of rules used to determine whether a number is divisible by another number without direct division.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 309 are 309, 618, 927, etc.

• Prime factors: The prime numbers that multiply together to give a composite number. For instance, the prime factors of 309 are 3 and 103.

• Subtraction: Subtraction is the process of finding the difference between two numbers by reducing one number from another.

• Integer: Integers are numbers that include all whole numbers, negative numbers, and zero.