Divisibility Rule of 780

The divisibility rule for 780 helps us find out if a number is divisible by 780 without using the division method. Let's check whether 1560 is divisible by 780 using this rule.

Step 1: Check divisibility by 10. The last digit of 1560 is 0, so it is divisible by 10.

Step 2: Check divisibility by 78. To do this, check divisibility by both 6 and 13, since 78 = 6 × 13.

Step 3: For divisibility by 6, check divisibility by both 2 and 3:
- 1560 is divisible by 2 because the last digit is 0 (an even number).
- Sum the digits of 1560 (1 + 5 + 6 + 0 = 12), which is divisible by 3.

Step 4: For divisibility by 13, use the rule: Multiply the last digit by 9 and subtract it from the rest of the number. Repeat if necessary:
- Multiply 0 by 9 (0 × 9 = 0), subtract from remaining digits (156 - 0 = 156).
- Multiply last digit of 156 by 9 (6 × 9 = 54), subtract from remaining digits (15 - 54 = -39), which is divisible by 13.

 

The divisibility rule for 780 helps us find out if a number is divisible by 780 without using the division method. Let's check whether 1560 is divisible by 780 using this rule.

Step 1: Check divisibility by 10. The last digit of 1560 is 0, so it is divisible by 10.

Step 2: Check divisibility by 78. To do this, check divisibility by both 6 and 13, since 78 = 6 × 13.

Step 3: For divisibility by 6, check divisibility by both 2 and 3:
- 1560 is divisible by 2 because the last digit is 0 (an even number).
- Sum the digits of 1560 (1 + 5 + 6 + 0 = 12), which is divisible by 3.

Step 4: For divisibility by 13, use the rule: Multiply the last digit by 9 and subtract it from the rest of the number. Repeat if necessary:
- Multiply 0 by 9 (0 × 9 = 0), subtract from remaining digits (156 - 0 = 156).
- Multiply last digit of 156 by 9 (6 × 9 = 54), subtract from remaining digits (15 - 54 = -39), which is divisible by 13.

Understanding divisibility rules can help students master division. Here are some tips and tricks for the divisibility rule of 780:

Know the factors of 780: Memorize the factorization (780 = 2 × 3 × 5 × 13) to quickly check divisibility.

Use negative numbers: If the subtraction yields a negative result, treat it as positive for checking divisibility.

Repeat the process for large numbers: Continue applying the divisibility rules until reaching a small enough number to verify divisibility.

Use the division method to verify: Use division as a way to cross-check results and reinforce learning.
 

• Divisibility rule: A set of rules to determine if a number is divisible by another number without performing division.

• Factors: Numbers that multiply together to produce another number. For example, 780 = 2 × 3 × 5 × 13.

• Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 780 are 780, 1560, 2340, etc.

• Integers: Whole numbers, including positive, negative numbers, and zero.

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