Divisibility Rule of 770

The divisibility rule for 770 is a method by which we can find out if a number is divisible by 770 or not without using the division method. To check whether a number is divisible by 770, it must be divisible by both 7, 11, and 10. Let's check whether 8470 is divisible by 770 using this rule.
 

Step 1: Check divisibility by 10. The number must end in 0. 8470 ends in 0, so it is divisible by 10.
 

Step 2: Check divisibility by 7. Multiply the last digit by 2, here the last digit is 0, so 0 × 2 = 0. Subtract this result from the remaining value, excluding the last digit: 847 - 0 = 847. Since 847 ÷ 7 = 121, the number is divisible by 7.
 

Step 3: Check divisibility by 11. Take the difference between the sum of the digits in odd positions and the sum of the digits in even positions: (8 + 7) - (4 + 0) = 15 - 4 = 11. Since 11 is divisible by 11, the number is divisible by 11.
 

Since 8470 is divisible by 7, 11, and 10, it is also divisible by 770.
 

Understanding the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 770.
 

• Know the multiples of 770:
  Memorize the multiples of 770 to quickly check divisibility. If a number is divisible by 7, 11, and 10, it is divisible by 770.
   
• Use the negative numbers:
  If the result we get after checking divisibility is negative, consider it positive for checking the divisibility.
   
• Repeat the process for large numbers:
  For large numbers, repeat the divisibility process until you simplify the number sufficiently. For example, check if 15400 is divisible by 770. It ends in 0, so it is divisible by 10.
  
  For 1540, multiply the last digit (0) by 2, 0 × 2 = 0, and subtract from the rest: 154 - 0 = 154. Since 154 ÷ 7 = 22, it is divisible by 7. For 154, (1 + 4) - 5 = 0, which is divisible by 11, so 15400 is divisible by 770.
   
• Use the division method to verify:
  Use the division method to verify and cross-check your results for better accuracy.

• Divisibility rule: The set of rules used to determine if a number is divisible by another number without performing division.
   
• Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 770 are 770, 1540, 2310, 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 from the other.
   
• Simplification: The process of reducing a number or expression to its simplest form.