Divisibility Rule of 735

The divisibility rule for 735 is a method by which we can find out if a number is divisible by 735 or not without using the division method. To check whether a number is divisible by 735, it must be divisible by its prime factors: 5, 21, and 7 (since 735 = 5 × 21 × 7). 

For example, check whether 5145 is divisible by 735 using its prime factors:

Step 1: Check divisibility by 5. The last digit must be 0 or 5. Since 5145 ends in 5, it is divisible by 5.

Step 2: Check divisibility by 21. A number is divisible by 21 if it is divisible by both 3 and 7. 

- Check divisibility by 3: Sum the digits of 5145 (5+1+4+5=15), and since 15 is divisible by 3, so is 5145.

- Check divisibility by 7 using the rule: Double the last digit and subtract from the rest. 514-10=504, then repeat: 50-8=42. Since 42 is divisible by 7, 504, and hence 5145, is divisible by 7.

Step 3: Since 5145 is divisible by 5, 3, and 7, it is divisible by 735.

Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 735.

Know the factors of 735:

Memorize that 735 = 5 × 21 × 7. For a number to be divisible by 735, it must be divisible by each of these factors.

Use divisibility rules for smaller factors:

If a number is divisible by 5, check for divisibility by 21 as a next step.

Repeat the process for large numbers:

Students should keep repeating the divisibility process until they reach a small number that is divisible by 735. For example, for a large number, first check divisibility by 5, then check divisibility by 21.

Use the division method to verify:

After using divisibility rules, verify your result with the division method for accuracy.

• Divisibility rule: A set of rules used to determine if one number is divisible by another.
   
• Factors: Numbers that divide another number exactly without leaving a remainder.
   
• Multiples: Results obtained by multiplying a number by an integer.
   
• Integers: Whole numbers including positive, negative numbers, and zero.
   
• Subtraction: The process of finding the difference between two numbers.