Divisibility Rule of 993

The divisibility rule for 993 is a method by which we can determine if a number is divisible by 993 without using the division method. Check whether 3969 is divisible by 993 with the divisibility rule.

Step 1: Break down 993 into its prime factors: 993 = 3 × 3 × 3 × 11.

Step 2: Ensure the number is divisible by each prime factor that makes up 993.

Check divisibility by 3: Add the digits of the number. If the sum is divisible by 3, then the number is divisible by 3.

Check divisibility by 11: Subtract the sum of the digits in odd positions from the sum of the digits in even positions. If the result is 0 or a multiple of 11, then the number is divisible by 11.

Step 3: If the number is divisible by both 9 (3 × 3) and 11, then it is divisible by 993.

For 3969:

- Add the digits: 3 + 9 + 6 + 9 = 27 (divisible by 3)
- Check for divisibility by 9: Since 27 is divisible by 9, 3969 is divisible by 9.
- Check for divisibility by 11: (3 + 6) - (9 + 9) = 9 - 18 = -9 (not a multiple of 11)

Therefore, 3969 is not divisible by 993.

Learn the divisibility rule to help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 993.

Know the prime factors:

Memorize the factors of 993 (3, 9, and 11) to quickly check divisibility. If a number is divisible by both 9 and 11, it is divisible by 993.

Use negative numbers:

If the result obtained after subtraction is negative, disregard the sign and consider it positive for checking divisibility.

Repeat the process for large numbers:

Students should keep repeating the divisibility process until they reach a small number that is divisible by 993. For example, check if 11979 is divisible by 993 using the divisibility test.

Add the digits: 1 + 1 + 9 + 7 + 9 = 27 (divisible by 3 and 9)
Check for divisibility by 11: (1 + 9 + 9) - (1 + 7) = 19 - 8 = 11 (a multiple of 11)
Since it satisfies divisibility for both 9 and 11, 11979 is divisible by 993.

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: The set of rules used to find out whether a number is divisible by another number or not.

• Prime factors: The prime numbers that multiply together to give the original number. For 993, these are 3 and 11.

• Multiples: The product obtained by multiplying a number by an integer. For instance, multiples of 993 are 993, 1986, etc.

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

• Integer: Whole numbers, including positive, negative numbers, and zero.