Divisibility Rule of 196

The divisibility rule for 196 allows us to determine if a number is divisible by 196 without performing actual division. Let's check if 1372 is divisible by 196 using the divisibility rule.

Step 1: Break down the number into smaller parts or use known rules for constituent factors of 196, such as 4 and 49 (since 196 = 4 × 49).

Step 2: Apply divisibility rules for each factor separately. For instance, check if 1372 is divisible by 4 and 49.

Divisibility by 4: A number is divisible by 4 if the last two digits form a number divisible by 4. In 1372, the last two digits are 72, which is divisible by 4.

Divisibility by 49: A number is divisible by 49 if the difference between twice the hundreds digit and the rest of the number is a multiple of 49. Here, twice the hundreds digit is 2×13=26, and the remaining number is 72. The difference 72-26=46 is not a multiple of 49, so 1372 is not divisible by 49.

Step 3: Since 1372 is not divisible by 49, it is not divisible by 196.

Understanding divisibility rules can help students master division. Here are some tips and tricks for the divisibility rule of 196:

• Know the factors of 196: Recognize that 196 is 4×49. Check divisibility by both factors.

• Use smaller divisibility rules: Apply the divisibility rules for 4 and 49 separately to simplify the process.

• Repeat the process for large numbers: For larger numbers, break down the problem into manageable steps by verifying divisibility by smaller factors.

• Use the division method to verify: Verify results with actual division to ensure accuracy.

• Divisibility rule: A set of guidelines to determine if a number can be divided by another without remainder.

• Factors: Numbers that multiply together to produce another number. For 196, they are 4 and 49.

• Multiples: The result of multiplying a number by an integer. For example, multiples of 196 include 196, 392, 588, etc.

• Integers: Whole numbers that can be positive, negative, or zero.

• Subtraction: The process of finding the difference between two numbers.