170 LearnersLast updated on May 26th, 2025
Divisibility Rule of 169
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 169.
What is the Divisibility Rule of 169?
The divisibility rule for 169 is a method by which we can find out if a number is divisible by 169 or not without using the division method. Check whether 2873 is divisible by 169 with the divisibility rule.
Step 1: Take the last two digits of the number, here in 2873, 73 is the last two digits.
Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last two digits. i.e., 28 - 73 = -45.
Step 3: If the result from Step 2 is a multiple of 169, or if after repeating the process it becomes 0 or a multiple of 169, then the number is divisible by 169. In this case, -45 is not a multiple of 169, so 2873 is not divisible by 169.
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Tips and Tricks for Divisibility Rule of 169
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 169.
- Know the multiples of 169: Memorize the multiples of 169 (169, 338, 507, 676, 845, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 169, then the number is divisible by 169.
- Use absolute values: If the result we get after the subtraction is negative, we will consider its absolute value for checking the divisibility of a number.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 169. For example, check if 3380 is divisible by 169 using the divisibility test. Take the last two digits, 80, and subtract from the remaining number, 33 - 80 = -47. Since -47 is not a multiple of 169, 3380 is not divisible by 169.
- Use the division method to verify: Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 169
The divisibility rule of 169 helps us to quickly check if the given number is divisible by 169, 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.
Students should follow the correct steps by taking the last two digits and subtracting it from the remaining digits. Then check whether it is a multiple of 169.
Mistake 2
Including the last two digits in subtraction.
Students should keep in mind to exclude the last two digits while subtracting and include all the remaining digits.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have a large number after subtraction. The process should be repeated until we get the smallest number that is divisible by 169.
Mistake 4
Not considering negative values.
Students should consider the absolute values when checking for divisibility, as the rule applies to negative values as well.
Mistake 5
Confusing the steps.
Students often confuse the steps or forget them, to avoid errors students should practice regularly.
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Divisibility Rule of 169 Examples
Problem 1
Is 28561 divisible by 169?
Yes, 28561 is divisible by 169.
Explanation
To determine if 28561 is divisible by 169, we can use the divisibility rule for 169, which involves breaking down the number.
1) Take the last three digits, which are 561.
2) Check if 561 is divisible by 169. Upon division, 561 ÷ 169 = 3.32, which is not an integer.
3) However, 28561 divided by 169 equals 169, confirming it is divisible.
Problem 2
Check if 33814 follows the divisibility rule of 169.
No, 33814 is not divisible by 169.
Explanation
To check the divisibility of 33814 by 169:
1) Take the last three digits, which are 814.
2) Check if 814 is divisible by 169. Upon division, 814 ÷ 169 ≈ 4.82, which is not an integer.
3) Therefore, 33814 is not divisible by 169.
Problem 3
Is -676 divisible by 169?
Yes, -676 is divisible by 169.
Explanation
To check if -676 is divisible by 169, we ignore the negative sign and check:
1) Take the number 676.
2) Divide 676 by 169. The result is 4, which is an integer.
3) Therefore, -676 is divisible by 169.
Problem 4
Can 12345 be divisible by 169 following the divisibility rule?
No, 12345 isn't divisible by 169.
Explanation
To determine if 12345 is divisible by 169:
1) Take the last three digits, which are 345.
2) Check if 345 is divisible by 169. Upon division, 345 ÷ 169 ≈ 2.04, which is not an integer.
3) Hence, 12345 is not divisible by 169.
Problem 5
Check the divisibility rule of 169 for 28730.
Yes, 28730 is divisible by 169.
Explanation
To check the divisibility of 28730 by 169:
1) Take the last three digits, which are 730.
2) Check if 730 is divisible by 169. Upon division, 730 ÷ 169 = 4.32, which is not an integer.
3) However, upon further inspection, 28730 divided by 169 equals 170, confirming that it is divisible.
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FAQs on Divisibility Rule of 169
1.What is the divisibility rule for 169?
2.How many numbers are there between 1 and 1000 that are divisible by 169?
3.Is 507 divisible by 169?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 169 apply to all integers?
6.How can children in Philippines use numbers in everyday life to understand Divisibility Rule of 169?
7.What are some fun ways kids in Philippines can practice Divisibility Rule of 169 with numbers?
8.What role do numbers and Divisibility Rule of 169 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Divisibility Rule of 169 skills?
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Important Glossaries for Divisibility Rule of 169
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 169 are 169, 338, 507, 676, etc.
- Integers: Integers include all whole numbers, negative numbers, and zero.
- Absolute value: The non-negative value of a number without regard to its sign.
- Subtraction: Subtraction is a process of finding the difference between two numbers, by reducing one number from another.
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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.
