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121 LearnersLast updated on February 18th, 2025
Divisibility Rule of 897
The divisibility rule is a way to determine whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 897.
What is the Divisibility Rule of 897?
The divisibility rule for 897 is a method by which we can find out if a number is divisible by 897 or not without using the division method.
Check whether 1794 is divisible by 897 with the divisibility rule.
Step 1: Break down 897 into its prime factors: 897 = 3 × 13 × 23.
Step 2: Check if 1794 is divisible by 3, 13, and 23 using their respective divisibility rules.
Divisibility by 3: The sum of the digits of 1794 is 1+7+9+4 = 21, which is divisible by 3.
Divisibility by 13: Double the last digit (4) and subtract it from the rest of the number: 179 - 8 = 171, which is divisible by 13.
Divisibility by 23: Multiply the last digit by 9 and subtract it from the rest: 179 - 36 = 143, which is divisible by 23.
Step 3: Since 1794 is divisible by 3, 13, and 23, it is divisible by 897.
Tips and Tricks for Divisibility Rule of 897
Learn divisibility rules to help master division. Let’s learn a few tips and tricks for the divisibility rule of 897.
Know the multiples of 897:
Memorize multiples of 897 (897, 1794, 2691, etc.) to quickly check divisibility.
Use the breakdown approach:
Always break down the number into prime factors to simplify checking divisibility.
Repeat the process for large numbers:
For larger numbers, repeat the divisibility checks for each factor until you reach a manageable size.
Use the division method to verify:
Use the division method to verify and cross-check results, reinforcing learning.
Common Mistakes and How to Avoid Them in Divisibility Rule of 897
The divisibility rule of 897 helps quickly check if a given number is divisible by 897, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Follow the correct steps by checking divisibility with each prime factor of 897.
Divisibility Rule of 897 Examples
Problem 1
Is 2691 divisible by 897?
No, 2691 is not divisible by 897.
Explanation
To determine if 2691 is divisible by 897, we break it down:
1) Divide 2691 by 897 directly: 2691 ÷ 897 ≈ 3.
2) The result is not an integer, indicating that 2691 is not divisible by 897.
Problem 2
Check the divisibility rule of 897 for 4485.
No, 4485 is not divisible by 897.
Explanation
For 4485, we check:
1) Divide 4485 by 897: 4485 ÷ 897 ≈ 5.
2) The result is not an integer, so 4485 is not divisible by 897.
Problem 3
Is 1794 divisible by 897?
Yes, 1794 is divisible by 897.
Explanation
To check if 1794 is divisible by 897:
1) Divide 1794 by 897: 1794 ÷ 897 = 2.
2) The result is an integer, thus 1794 is divisible by 897.
Problem 4
Can -897 be divisible by 897?
Yes, -897 is divisible by 897.
Explanation
A negative number can still be divisible:
1) Divide -897 by 897: -897 ÷ 897 = -1.
2) The result is an integer, so -897 is divisible by 897.
Problem 5
Check the divisibility rule of 897 for 0.
Yes, 0 is divisible by 897.
Explanation
Any number can divide 0:
1) Divide 0 by 897: 0 ÷ 897 = 0.
2) The result is an integer, confirming 0 is divisible by 897.
FAQs on Divisibility Rule of 897
1.What is the divisibility rule for 897?
2.How many numbers are there between 1 and 5000 that are divisible by 897?
3.Is 2691 divisible by 897?
4.What if I get 0 after subtraction?
5.Does the divisibility rule of 897 apply to all integers?
Important Glossaries for Divisibility Rule of 897
- Divisibility rule: A set of guidelines to determine if a number is divisible by another number without performing division.
- Prime factors: Prime numbers that multiply together to give the original number (e.g., 897 = 3 × 13 × 23).
- Multiples: Numbers obtained by multiplying a number by an integer (e.g., multiples of 897 are 897, 1794, etc.).
- Subtraction: The process of taking one number away from another to find the difference.
- Verification: The act of confirming whether a calculation or result is correct, often by using a different method.
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
