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124 LearnersLast updated on February 17th, 2025
Divisibility Rule of 840
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 840.
What is the Divisibility Rule of 840?
The divisibility rule for 840 involves checking divisibility by its prime factors: 2, 3, 5, and 7. A number is divisible by 840 if it is divisible by all of these factors.
Example: Check whether 2520 is divisible by 840 using its divisibility rule.
- Check for 2: The last digit is 0, which is even, so it is divisible by 2.
- Check for 3: Sum of digits is 2+5+2+0 = 9, which is divisible by 3.
- Check for 5: The last digit is 0, which is divisible by 5.
- Check for 7: Use the rule of 7 (explained below). Here, you can verify that 2520 is divisible by 7.
Since 2520 is divisible by 2, 3, 5, and 7, it is divisible by 840.
Tips and Tricks for Divisibility Rule of 840
1. Know the prime factors:
Memorize the prime factors of 840 (2, 3, 5, 7) and check for divisibility by each.
2. Use divisibility rules for each factor:
- For 2, check if the last digit is even.
- For 3, sum the digits and check if the sum is divisible by 3.
- For 5, check if the last digit is 0 or 5.
- For 7, double the last digit, subtract from the rest, and check divisibility.
3. Repeat as needed:
If a number is large, verify divisibility by each factor systematically.
4. Verify with division:
Use division to confirm results and cross-check your work.
Common Mistakes and How to Avoid Them in Divisibility Rule of 840
here are soe mistakes with their solutions are given.
Mistake 1
Not checking all factors.
Ensure to check divisibility by 2, 3, 5, and 7.
Divisibility Rule of 840 Examples
Problem 1
Is the number of chairs in a large conference room, 1680, divisible by 840?
Yes, 1680 is divisible by 840
Explanation
To check if 1680 is divisible by 840, we need to check divisibility by 8, 4, and 10 (since 840 = 8 x 4 x 10):
1) Check divisibility by 8: The last three digits, 680, are divisible by 8 (680 ÷ 8 = 85).
2) Check divisibility by 4: The last two digits, 80, are divisible by 4 (80 ÷ 4 = 20).
3) Check divisibility by 10: The last digit is 0, which means it is divisible by 10.
Since 1680 satisfies all these conditions, it is divisible by 840.
Problem 2
A shipment contains 2520 units of merchandise. Can this number of units be evenly divided into groups of 840?
Yes, 2520 is divisible by 840.
Explanation
To determine if 2520 is divisible by 840, check divisibility by 8, 4, and 10:
1) Check divisibility by 8: The last three digits, 520, are divisible by 8 (520 ÷ 8 = 65).
2) Check divisibility by 4: The last two digits, 20, are divisible by 4 (20 ÷ 4 = 5).
3) Check divisibility by 10: The last digit is 0, so it is divisible by 10.
Since 2520 meets all these criteria, it is divisible by 840.
Problem 3
A library acquires 3360 new books. Can these books be organized in rows of 840?
Yes, 3360 is divisible by 840.
Explanation
To verify if 3360 is divisible by 840, we check divisibility by 8, 4, and 10:
1) Check divisibility by 8: The last three digits, 360, are divisible by 8 (360 ÷ 8 = 45).
2) Check divisibility by 4: The last two digits, 60, are divisible by 4 (60 ÷ 4 = 15).
3) Check divisibility by 10: The last digit is 0, which means it is divisible by 10.
Since all conditions are met, 3360 is divisible by 840.
Problem 4
A box of chocolates contains 980 pieces. Can these be evenly divided into trays with 840 chocolates each?
No, 980 is not divisible by 840.
Explanation
To determine if 980 is divisible by 840, check divisibility by 8, 4, and 10:
1) Check divisibility by 8: The last three digits, 980, are not divisible by 8 (980 ÷ 8 = 122.5).
2) Check divisibility by 4: The last two digits, 80, are divisible by 4 (80 ÷ 4 = 20).
3) Check divisibility by 10: The last digit is 0, so it is divisible by 10.
Since 980 is not divisible by 8, it is not divisible by 840.
Problem 5
A factory produces 5040 widgets in a week. Can these widgets be grouped into batches of 840?
Yes, 5040 is divisible by 840
Explanation
To check if 5040 is divisible by 840, ensure divisibility by 8, 4, and 10:
1) Check divisibility by 8: The last three digits, 040, are divisible by 8 (040 ÷ 8 = 5).
2) Check divisibility by 4: The last two digits, 40, are divisible by 4 (40 ÷ 4 = 10).
3) Check divisibility by 10: The last digit is 0, indicating divisibility by 10.
Since 5040 satisfies all these conditions, it is divisible by 840.
FAQs on Divisibility Rule of 840
1.What is the divisibility rule for 840?
2.How many numbers between 1 and 1000 are divisible by 840?
3. Is 1680 divisible by 840?
4. What if a number is not divisible by one of the factors?
5.Does the divisibility rule of 840 apply to all integers?
Important Glossaries for Divisibility Rule of 840
- Divisibility rule: A set of guidelines to determine if a number can be divided by another number without a remainder.
- Prime factors: The prime numbers that multiply together to form a given number.
- Multiples: The results obtained by multiplying a number by an integer.
- Even numbers: Numbers divisible by 2, with the last digit being 0, 2, 4, 6, or 8.
- Division method: A mathematical process to determine how many times one number is contained within 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.
