Last updated on May 26th, 2025
The divisibility rule is a way to determine whether a number is divisible by another number without performing division directly. In real life, divisibility rules help with quick calculations, dividing items evenly, and organizing tasks. In this topic, we will explore the divisibility rule for 561.
The divisibility rule for 561 is a method to check if a number is divisible by 561 without dividing. Let's examine whether 1683 is divisible by 561 using this rule.
Step 1: Multiply the last digit of the number by a factor, specific to 561. (For example, if the factor is 3, multiply the last digit by 3.)
Here, in 1683, the last digit is 3. Multiply it by 3: 3 × 3 = 9.
Step 2: Subtract the result from Step 1 from the remaining number, excluding the last digit. For example, 168 - 9 = 159.
Step 3: Check if the result (159 in this case) is divisible by 561. If it is, then the original number is divisible by 561. If it's not, then the original number isn't divisible by 561.
Knowing the divisibility rule helps simplify division. Here are some tips and tricks for understanding the divisibility rule of 561:
Understanding the divisibility rule of 561 can prevent errors, but common mistakes can occur. Here are some to watch out for:
Is 1122 divisible by 561?
Yes, 1122 is divisible by 561.
To check if 1122 is divisible by 561, we can apply the divisibility rule for 561. Since 561 is a composite number, we check divisibility by its prime factors (3, 11, and 17).
1) Check divisibility by 3: The sum of the digits is 1 + 1 + 2 + 2 = 6, which is divisible by 3.
2) Check divisibility by 11: The alternating sum of the digits is 1 - 1 + 2 - 2 = 0, which is divisible by 11.
3) Check divisibility by 17: 1122 ÷ 17 = 66, which is an integer, so 1122 is divisible by 17.
Since 1122 is divisible by 3, 11, and 17, it is divisible by 561.
Can 1683 be divisible by 561 using the divisibility rule?
Yes, 1683 is divisible by 561.
We need to verify divisibility by the factors of 561, which are 3, 11, and 17.
1) Divisibility by 3: The sum of the digits is 1 + 6 + 8 + 3 = 18, which is divisible by 3.
2) Divisibility by 11: The alternating sum of the digits is 1 - 6 + 8 - 3 = 0, which is divisible by 11.
3) Divisibility by 17: 1683 ÷ 17 = 99, which is an integer, so 1683 is divisible by 17.
Since 1683 is divisible by 3, 11, and 17, it is divisible by 561.
Check the divisibility rule of 561 for -3366.
Yes, -3366 is divisible by 561.
We remove the negative sign and check the divisibility by factors of 561: 3, 11, and 17.
1) Divisibility by 3: The sum of the digits is 3 + 3 + 6 + 6 = 18, which is divisible by 3.
2) Divisibility by 11: The alternating sum of the digits is 3 - 3 + 6 - 6 = 0, which is divisible by 11.
3) Divisibility by 17: 3366 ÷ 17 = 198, which is an integer, so 3366 is divisible by 17.
Since 3366 is divisible by 3, 11, and 17, it is divisible by 561.
Is 252 divisible by 561 using the divisibility rule?
No, 252 is not divisible by 561.
We check divisibility by the factors of 561: 3, 11, and 17.
1) Divisibility by 3: The sum of the digits is 2 + 5 + 2 = 9, which is divisible by 3.
2) Divisibility by 11: The alternating sum of the digits is 2 - 5 + 2 = -1, which is not divisible by 11.
3) Divisibility by 17: 252 ÷ 17 = 14.8235, which is not an integer.
Since 252 is not divisible by 11 or 17, it is not divisible by 561.
Verify if 5610 is divisible by 561 using the rule.
Yes, 5610 is divisible by 561.
We check divisibility by the factors of 561: 3, 11, and 17.
1) Divisibility by 3: The sum of the digits is 5 + 6 + 1 + 0 = 12, which is divisible by 3.
2) Divisibility by 11: The alternating sum of the digits is 5 - 6 + 1 - 0 = 0, which is divisible by 11.
3) Divisibility by 17: 5610 ÷ 17 = 330, which is an integer.
Since 5610 is divisible by 3, 11, and 17, it is divisible by 561.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.