Divisibility Rule of 354

The divisibility rule for 354 is a method by which we can determine if a number is divisible by 354 without using the division method. 

Check whether 708 is divisible by 354 using the divisibility rule.

Step 1: Check divisibility by 2. The last digit of 708 is 8, which is even, so it is divisible by 2.

Step 2: Check divisibility by 3. Sum the digits of 708: 7 + 0 + 8 = 15. Since 15 is divisible by 3, 708 is divisible by 3.

Step 3: Check divisibility by 59. Use a calculator or long division to verify if 708 is exactly divisible by 59. In this case, 708 ÷ 59 = 12, which is an integer, so 708 is divisible by 59.

Since 708 is divisible by 2, 3, and 59, it is divisible by 354.

Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 354.

Know the factors of 354:

Memorize the factors of 354 (2, 3, and 59) to quickly check divisibility. If a number is divisible by all these factors, it is divisible by 354.

Use divisibility tests for smaller factors:

First, check divisibility by smaller factors like 2 and 3, as these are quicker to verify before moving to larger factors like 59.

Use technology for larger numbers:

For checking divisibility by larger numbers (like 59 in this case), use a calculator or long division to verify.

Repeat the process for large numbers:

For large numbers, continue using the divisibility tests of all factors until you confirm divisibility by all, ensuring the number is divisible by 354.

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 to verify and also learn.

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

• Factors: Numbers that divide another number exactly without leaving a remainder. For example, factors of 354 are 2, 3, and 59.

• Integers: Whole numbers that include positive numbers, negative numbers, and zero.

• Sum: The result of adding numbers together. Used for checking divisibility by 3.

• Division: The process of determining how many times one number is contained within another. Used for verifying divisibility.