Last updated on May 26th, 2025
The divisibility rule is a way to determine whether a number is divisible by another number without resorting to direct division. 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 426.
The divisibility rule for 426 is a method by which we can find out if a number is divisible by 426 without using long division. Check whether 852 is divisible by 426 using the divisibility rule.
Step 1: Check if the number is divisible by 2, 3, and 71 (the prime factors of 426).
- Divisibility by 2: The number must be even. 852 is even.
- Divisibility by 3: The sum of the digits must be divisible by 3. The sum of the digits of 852 is 8 + 5 + 2 = 15, which is divisible by 3.
- Divisibility by 71: For larger numbers, use direct division or the multiplication method. Divide 852 by 71, resulting in 12, which is a whole number.
Step 2: As 852 is divisible by 2, 3, and 71, it is divisible by 426.
Learning the divisibility rule can help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 426.
Memorize the multiples of 426 (426, 852, 1278, etc.) to quickly check divisibility. If the result from checking divisibility by 2, 3, and 71 confirms divisibility, then the number is divisible by 426.
Break down the checks using the prime factors of 426 to determine divisibility.
For larger numbers, repeat the divisibility checks for 2, 3, and 71 until you confirm divisibility.
Students can use direct division as a way to verify and cross-check their results. This will help them to verify and also learn.
The divisibility rule of 426 helps us to quickly check if a given number is divisible by 426, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Is the weight of a shipment, 852 kg, divisible by 426?
Yes, 852 kg is divisible by 426.
To check if 852 is divisible by 426, we need to divide the number directly since there isn’t a simple rule for 426 like there is for smaller numbers.
1) Divide 852 by 426.
2) 852 ÷ 426 = 2.
3) The result is a whole number, so 852 is divisible by 426.
A parking lot can hold 426 cars in one section. If the total capacity is 1704 cars, can each section be filled evenly?
Yes, each section can be filled evenly with 1704 cars.
To verify if 1704 can be divided evenly among sections of 426 cars:
1) Divide 1704 by 426.
2) 1704 ÷ 426 = 4.
3) This results in a whole number, indicating that the cars can be evenly distributed across the sections.
A factory produces 1278 widgets in a day and needs to pack them into crates that hold 426 widgets each. Can all the widgets be packed without any left over?
No, 1278 widgets cannot be packed perfectly into crates of 426.
To determine if 1278 widgets can be divided into crates of 426:
1) Divide 1278 by 426.
2) 1278 ÷ 426 = 3 with a remainder.
3) The division does not result in a whole number, so there will be leftover widgets.
A school is organizing a field trip for 2556 students, and each bus can carry 426 students. Can all students be accommodated without any leftover?
Yes, all students can be accommodated.
To see if 2556 students can be divided into groups of 426:
1) Divide 2556 by 426.
2) 2556 ÷ 426 = 6.
3) The result is a whole number, meaning all students can be accommodated without any leftover.
A wholesaler has 6390 items to distribute equally among 426 stores. Can each store receive the same number of items?
No, each store cannot receive the same number of items without leftovers.
To determine if 6390 items can be evenly distributed among 426 stores:
1) Divide 6390 by 426.
2) 6390 ÷ 426 = 15 with a remainder.
3) The division does not result in a whole number, so there will be leftover items.
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.
: She loves to read number jokes and games.