Divisibility Rule of 840

The divisibility rule for 840 involves checking divisibility by its prime factors: 2, 3, 5, and 7. A number is divisible by 840 if it is divisible by all of these factors.

Example: Check whether 2520 is divisible by 840 using its divisibility rule.

- Check for 2: The last digit is 0, which is even, so it is divisible by 2.

- Check for 3: Sum of digits is 2+5+2+0 = 9, which is divisible by 3.

- Check for 5: The last digit is 0, which is divisible by 5.

- Check for 7: Use the rule of 7 (explained below). Here, you can verify that 2520 is divisible by 7.

Since 2520 is divisible by 2, 3, 5, and 7, it is divisible by 840.

1. Know the prime factors:

Memorize the prime factors of 840 (2, 3, 5, 7) and check for divisibility by each.

2. Use divisibility rules for each factor:

   - For 2, check if the last digit is even.
   - For 3, sum the digits and check if the sum is divisible by 3.
   - For 5, check if the last digit is 0 or 5.
   - For 7, double the last digit, subtract from the rest, and check divisibility.

3. Repeat as needed:

If a number is large, verify divisibility by each factor systematically.

4. Verify with division:

Use division to confirm results and cross-check your work.
 

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

• Prime factors: The prime numbers that multiply together to form a given number.

• Multiples: The results obtained by multiplying a number by an integer.

• Even numbers: Numbers divisible by 2, with the last digit being 0, 2, 4, 6, or 8.

• Division method: A mathematical process to determine how many times one number is contained within another.