180 LearnersLast updated on May 26th, 2025
Divisibility Rule of 174
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 174.
What is the Divisibility Rule of 174?
The divisibility rule for 174 is a method by which we can determine if a number is divisible by 174 without using the division method. Check whether 348 is divisible by 174 with the divisibility rule.
Step 1: Check if the number is even. 348 is even, so proceed to the next step.
Step 2: Check if the sum of the digits is divisible by 3. For 348, the sum of the digits is 3 + 4 + 8 = 15, which is divisible by 3.
Step 3: Check if the number ends in 0, 4, or 8. Since 348 ends in 8, it satisfies this rule.
Since all conditions are satisfied, 348 is divisible by 174.
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Tips and Tricks for Divisibility Rule of 174
Learn divisibility rules to help master division. Let’s learn a few tips and tricks for the divisibility rule of 174.
- Know the multiples of 174: Memorize the multiples of 174 (174, 348, 522, 696, 870…etc.) to quickly check divisibility. If a number matches one of these, it is divisible by 174.
- Use basic divisibility rules: Since 174 is 2 × 3 × 29, you can check divisibility by these factors separately. Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 174. For example, check if 1044 is divisible by 174. Since 1044 is even, its digit sum is 9 (which is divisible by 3), and it ends in 4, it is divisible by 174.
- Use the division method to verify: Students can use the division method to verify and cross-check their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 174
The divisibility rule of 174 helps us to quickly check if a given number is divisible by 174, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, checking if the number is even, the sum of the digits is divisible by 3, and the last digit meets the criteria (0, 4, or 8).
Mistake 2
Ignoring one of the criteria.
Ensure all conditions of the rule are met: even numbers, a digit sum divisible by 3, and the correct ending digit.
Mistake 3
Not repeating the process for large numbers.
Students often stop the process after checking once. The process should be repeated until a small divisible number is confirmed.
Mistake 4
Not considering the basic factors.
Remember that since 174 is a composite number (2 × 3 × 29), its divisibility criteria are based on these factors.
Mistake 5
Confusing the steps.
To avoid this error, students should practice regularly and memorize the steps.
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Divisibility Rule of 174 Examples
Problem 1
Is 522 divisible by 174?
Yes, 522 is divisible by 174.
Explanation
To verify if 522 is divisible by 174, follow these steps:
1) Divide 522 by 174, which results in exactly 3.
2) Since the result is a whole number without a remainder, 522 is divisible by 174.
Problem 2
Check the divisibility rule of 174 for 696.
Yes, 696 is divisible by 174.
Explanation
To check the divisibility of 696 by 174:
1) Divide 696 by 174, which equals 4.
2) As the division results in a whole number, 696 is divisible by 174.
Problem 3
Is 870 divisible by 174?
No, 870 is not divisible by 174.
Explanation
To determine if 870 is divisible by 174:
1) Divide 870 by 174, which results in approximately 5.
2) Since the result is not an integer, 870 is not divisible by 174.
Problem 4
Can 348 be divisible by 174 using the divisibility rule?
Yes, 348 is divisible by 174.
Explanation
To check if 348 is divisible by 174:
1) Divide 348 by 174, which results in exactly 2.
2) As the division results in a whole number, 348 is divisible by 174.
Problem 5
Check the divisibility rule of 174 for 1044.
Yes, 1044 is divisible by 174.
Explanation
To verify if 1044 is divisible by 174:
1) Divide 1044 by 174, which results in exactly 6.
2) Since the division results in a whole number, 1044 is divisible by 174.
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FAQs on Divisibility Rule of 174
1.What is the divisibility rule for 174?
2.How many numbers are there between 1 and 1000 that are divisible by 174?
3.Is 522 divisible by 174?
4.What if I get 0 after checking all criteria?
5.Does the divisibility rule of 174 apply to all integers?
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Important Glossaries for Divisibility Rule of 174
- Divisibility rule: The set of guidelines used to determine whether a number is divisible by another number without performing division.
- Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 174 are 174, 348, 522, etc.
- Even number: A number divisible by 2, ending in 0, 2, 4, 6, or 8.
- Digit sum: The sum of all digits in a number, used in checking divisibility by certain numbers.
- Integer: Whole numbers that include positive numbers, negative numbers, and zero.
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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.
