Divisibility Rule of 238

The divisibility rule for 238 is a method by which we can find out if a number is divisible by 238 without using direct division. Let's check whether 4760 is divisible by 238 using the divisibility rule.

Step 1: Break down the number 238 into its prime factors: 2, 7, and 17. A number must be divisible by each of these factors to be divisible by 238.

Step 2: Check if 4760 is divisible by 2, 7, and 17.

- Divisibility by 2: The last digit of 4760 is 0, which is even, so it is divisible by 2.
- Divisibility by 7: Use the rule for 7. Double the last digit and subtract from the rest: 476 - 0 = 476. Since 476 is divisible by 7, so is 4760.
- Divisibility by 17: Divide 4760 by 17. If it results in an integer, it’s divisible by 17.

Step 3: Since 4760 is divisible by 2, 7, and 17, it is divisible by 238.
 

Understanding the divisibility rule helps in mastering division. Here are some tips and tricks for the divisibility rule of 238:

Memorize the prime factors:

Knowing the prime factors (2, 7, and 17) will aid in quickly checking divisibility.

Use factorization:

Factorize the number into these prime factors to verify divisibility.

Repeat for large numbers:

For large numbers, break them into smaller parts that are easier to check for divisibility by 2, 7, and 17.

Verify using division:

After using the divisibility rule, verify by division to ensure accuracy.
 

• Divisibility rule: A set of rules used to determine if a number is divisible by another without direct division.

• Prime factors: Prime numbers that multiply together to give the original number (e.g., 2, 7, and 17 are prime factors of 238).

• Integer: A whole number that can be positive, negative, or zero.

• Factorization: The process of breaking down a number into its prime factors.

• Remainder: The amount left over after division when a number does not divide evenly.