Divisibility Rule of 313

The divisibility rule for 313 is a method by which we can determine if a number is divisible by 313 without directly dividing. Check whether 203,569 is divisible by 313 using this rule.  

Step 1: Take the last three digits of the number, here in 203,569, which are 569.

Step 2: Subtract 3 times this value from the rest of the number, i.e., 203 - 3 × 569.

Step 3: Calculate 203 - 1707 = -1504.

Step 4: If the result is a multiple of 313, then the original number is divisible by 313. If not, it is not divisible.

Learning the divisibility rule can help students master division. Let’s explore some tips and tricks for the divisibility rule of 313.

Know the multiples of 313:

Memorize the multiples of 313 (313, 626, 939, ...etc.) to quickly check divisibility. If the result from subtraction is a multiple of 313, then the number is divisible by 313.

Use negative numbers:

If the subtraction result is negative, consider its absolute value to check divisibility.

Repeat the process for large numbers:

Students should keep repeating the divisibility process until they reach a small number that is easily recognizable as a multiple of 313. For example, check if 94,513 is divisible by 313 using the divisibility test. Take the last three digits, which is 513, and calculate 94 - 3 × 513 = 94 - 1539 = -1445. Repeat the process: Take the absolute value, 1445, and do 1 - 3 × 445 = 1 - 1335 = -1334. Since -1334 is not a multiple of 313, 94,513 is not divisible by 313.

Use the division method to verify:

Students can use the division method to verify their results. This will help them confirm their understanding.

• Divisibility rule: A set of rules used to determine whether a number is divisible by another number.

• Multiples: Numbers that result from multiplying a number by an integer. For example, multiples of 313 are 313, 626, 939, etc.

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

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

• Absolute value: The non-negative value of a number without regard to its sign.