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113 LearnersLast updated on February 17th, 2025
Divisibility Rule of 852
The divisibility rule is a way to find out 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 852.
What is the Divisibility Rule of 852?
The divisibility rule for 852 is a method by which we can find out if a number is divisible by 852 or not without using the division method. Check whether 1704 is divisible by 852 with the divisibility rule.
Step 1: Check if the number is divisible by 2, 3, and 71 (since 852 = 2 × 3 × 71).
Step 2: 1704 ends in 4, which is even, so it is divisible by 2.
Step 3: Add the digits of 1704 (1 + 7 + 0 + 4 = 12). Since 12 is divisible by 3, 1704 is divisible by 3.
Step 4: Now, check divisibility by 71. This is more complex, so for simplicity, you may need to use a calculator or division for this step.
Step 5: If 1704 is divisible by 71, then it is divisible by 852. In this case, 1704 is not divisible by 71, so it is not divisible by 852.
Tips and Tricks for Divisibility Rule of 852
Learn divisibility rules to help master division. Let’s learn a few tips and tricks for the divisibility rule of 852.
1. Know the prime factors:
Memorize the prime factors of 852 (2, 3, and 71) to quickly check divisibility
2. Use divisibility rules for smaller numbers:
Check divisibility by 2 and 3 easily using their rules, and then proceed to 71.
3. Repeat the process for large numbers:
For large numbers, break them down and check divisibility for each factor. If a number is large, use a calculator for checking divisibility by 71
4. Verify using division:
Use the division method to verify and crosscheck results. This will help in learning and confirming divisibility.
Common Mistakes and How to Avoid Them in Divisibility Rule of 852
The divisibility rule of 852 helps us to quickly check if the given number is divisible by 852, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking all prime factors.
Ensure the number is divisible by 2, 3, and 71 to confirm divisibility by 852.
Divisibility Rule of 852 Examples
Problem 1
Is 2556 divisible by 852?
No, 2556 is not divisible by 852.
Explanation
To check for divisibility by 852, we need to understand that 852 is the product of the prime factors 2, 3, and 71. Therefore, a number must be divisible by these to be divisible by 852.
1) Check divisibility by 2: 2556 is even, so it passes.
2) Check divisibility by 3: Sum the digits (2 + 5 + 5 + 6 = 18), which is divisible by 3.
3) Check divisibility by 71: Divide 2556 by 71, which results in a non-integer. Therefore, 2556 is not divisible by 71, and hence not by 852.
Problem 2
Check if 6822 is divisible by 852.
No, 6822 is not divisible by 852.
Explanation
To determine if 6822 is divisible by 852, we use the prime factors 2, 3, and 71:
1) Divisibility by 2: 6822 is even, so it passes.
2) Divisibility by 3: Sum the digits (6 + 8 + 2 + 2 = 18), which is divisible by 3.
3) Divisibility by 71: Divide 6822 by 71, which gives a non-integer. Thus, 6822 is not divisible by 71, and therefore not by 852.
Problem 3
Is 1704 divisible by 852?
Yes, 1704 is divisible by 852.
Explanation
To confirm divisibility by 852, check the prime factors:
1) Divisibility by 2: 1704 is even, so it passes.
2) Divisibility by 3: Sum the digits (1 + 7 + 0 + 4 = 12), which is divisible by 3.
3) Divisibility by 71: Divide 1704 by 71, which results in an integer (24). Therefore, 1704 is divisible by all factors and by 852.
Problem 4
Can 3416 be divisible by 852 using its divisibility rule?
No, 3416 is not divisible by 852.
Explanation
Check divisibility using 852's prime factors:
1) Divisibility by 2: 3416 is even, so it passes.
2) Divisibility by 3: Sum the digits (3 + 4 + 1 + 6 = 14), which is not divisible by 3.
Since 3416 fails the divisibility test for 3, it is not divisible by 852.
Problem 5
Verify if 25560 is divisible by 852.
Yes, 25560 is divisible by 852.
Explanation
Check divisibility through prime factors:
1) Divisibility by 2: 25560 is even, so it passes.
2) Divisibility by 3: Sum the digits (2 + 5 + 5 + 6 + 0 = 18), which is divisible by 3.
3) Divisibility by 71: Divide 25560 by 71, which results in an integer (360). Therefore, 25560 is divisible by all factors and by 852.
FAQs on Divisibility Rule of 852
1. What is the divisibility rule for 852?
2. How many numbers are there between 1 and 1000 that are divisible by 852?
3. Is 1704 divisible by 852?
4.What if I get a remainder when dividing by one of the factors?
5.Does the divisibility rule of 852 apply to all integers?
Important Glossaries for Divisibility Rule of 852
- Divisibility Rule: A method to determine if one number is divisible by another without performing full division.
- Prime Factors: The prime numbers that multiply together to give the original number (e.g., 2, 3, and 71 for 852).
- Remainder: The amount left over after division when one number doesn't divide the other exactly.
- Integer: A whole number that can be positive, negative, or zero.
- Multiples: Numbers obtained by multiplying a given number by integers (e.g., multiples of 852 are 852, 1704, 2556...).
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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.
