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119 LearnersLast updated on February 18th, 2025
Divisibility Rule of 977
The divisibility rule is a method to determine if a number is divisible by another number without performing the division operation. 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 977.
What is the Divisibility Rule of 977?
The divisibility rule for 977 is a method by which we can determine if a number is divisible by 977 without using the division method. Check whether 1954 is divisible by 977 with the divisibility rule.
Step 1: Since 977 is a large number, there is no simple shortcut like with smaller primes. The best method is to directly check divisibility using division or a calculator.
Step 2: Division of 1954 by 977 gives a quotient that is not an integer (1954 ÷ 977 ≈ 2.000), indicating 1954 is not divisible by 977.
Tips and Tricks for Divisibility Rule of 977
Learn the divisibility rule to master division. Let’s learn a few tips and tricks for the divisibility rule of 977.
Know the multiples of 977:
Memorize the first few multiples of 977 (977, 1954, 2931, etc.) to quickly check divisibility. If your number matches one of these multiples, it's divisible by 977.
Use a calculator:
Given the size of 977, using a calculator or performing long division is often the most efficient method to check divisibility.
Repeat the process for larger numbers:
For very large numbers, first check with known multiples of 977 and then use division for confirmation.
Use the division method to verify:
Always verify divisibility by performing the division to confirm your result.
Common Mistakes and How to Avoid Them in Divisibility Rule of 977
The divisibility rule of 977 helps us quickly check if a given number is divisible by 977, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not using precise tools.
For larger divisors like 977, always use a calculator or precise mathematical tools to avoid errors.
Divisibility Rule of 977 Examples
Problem 1
Is 4885 divisible by 977?
No, 4885 is not divisible by 977.
Explanation
To check the divisibility of 4885 by 977,
1) Multiply the last digit by 5, 5 × 5 = 25.
2) Subtract the result from the remaining number, 488 - 25 = 463.
3) Since 463 is not zero and not a multiple of 977, 4885 is not divisible by 977.
Problem 2
Check the divisibility of 1954 by 977.
Yes, 1954 is divisible by 977.
Explanation
To verify 1954's divisibility by 977,
1) Multiply the last digit by 5, 4 × 5 = 20.
2) Subtract this from the remaining part of the number, 195 - 20 = 175.
3) Check if 175 is zero or a multiple of 977.
Since 1954 is exactly twice 977, it is divisible by 977.
Problem 3
Is -2931 divisible by 977?
No, -2931 is not divisible by 977.
Explanation
Checking divisibility for -2931 by 977,
1) Remove the negative sign to work with 2931.
2) Multiply the last digit by 5, 1 × 5 = 5.
3) Subtract this from the rest, 293 - 5 = 288.
4) Since 288 is not zero and not a multiple of 977, -2931 is not divisible by 977.
Problem 4
Can 977 be divisible by 977?
Yes, 977 is divisible by 977.
Explanation
Any number is divisible by itself. Since 977 divided by 977 equals 1, it is divisible by 977.
Problem 5
Determine if 19540 is divisible by 977.
No, 19540 is not divisible by 977.
Explanation
To determine divisibility,
1) Multiply the last digit by 5, 0 × 5 = 0.
2) Subtract from the rest of the number, 1954 - 0 = 1954.
3) Check if 1954 is divisible by 977.
Since it isn’t zero and 1954 is not a multiple of 977, 19540 is not divisible by 977.
FAQs on Divisibility Rule of 977
1.What is the divisibility rule for 977?
2.How many numbers are there between 1 and 1000 that are divisible by 977?
3.Is 2931 divisible by 977?
4.What if I get a remainder after dividing?
5.Does the divisibility rule of 977 apply to all integers?
Important Glossaries for Divisibility Rule of 977
- Divisibility: The ability for one number to be divided by another number without any remainder.
- Multiples: Results obtained by multiplying a number by integers. For example, multiples of 977 are 977, 1954, 2931, etc.
- Integers: Whole numbers that include positive numbers, negative numbers, and zero.
- Division: The process of determining how many times one number is contained within another.
- Remainder: The amount left over after division when a number does not divide evenly.
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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.
