Last updated on May 26th, 2025
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 56.
The divisibility rule for 56 is a method by which we can find out if a number is divisible by 56 or not without using the division method. Check whether 1232 is divisible by 56 using the divisibility rule.
Step 1: Check if the number is divisible by both 7 and 8, as 56 = 7 × 8.
Step 2: For divisibility by 7, multiply the last digit by 2, and subtract it from the rest of the number. If the result is a multiple of 7, then it is divisible by 7. For 1232, the last digit is 2, so 2 × 2 = 4. Subtract 4 from 123, which gives 119. Since 119 is divisible by 7, 1232 is divisible by 7.
Step 3: For divisibility by 8, check if the last three digits of the number form a number divisible by 8. In this case, 232 is not divisible by 8. Therefore, 1232 is not divisible by 56.
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 56.
The divisibility rule of 56 helps us to quickly check if the given number is divisible by 56, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Is the number of students in a class, 168, divisible by 56?
Yes, 168 is divisible by 56.
To check if 168 is divisible by 56, we can use the divisibility rule:
1) First, check the divisibility of 168 by both 8 and 7 (since 56 = 8 x 7).
2) For 8, the last three digits of 168 are 168, and 168 ÷ 8 = 21, so it's divisible by 8.
3) For 7, follow the rule: Multiply the last digit by 2, 8 × 2 = 16. Subtract from the rest, 16 – 16 = 0.
4) Since the result is 0, 168 is divisible by 7.
5) As 168 is divisible by both 8 and 7, it is divisible by 56.
A bakery produces 224 cookies, determine if this number is divisible evenly among 56 friends.
Yes, 224 is divisible by 56.
To determine if 224 is divisible by 56, we check its divisibility by both 8 and 7.
1) For 8: The last three digits are 224, and 224 ÷ 8 = 28, so it's divisible by 8.
2) For 7: Multiply the last digit by 2, 4 × 2 = 8. Subtract from the rest, 22 – 8 = 14.
3) Since 14 is a multiple of 7, 224 is divisible by 7.
4) As 224 is divisible by both 8 and 7, it is divisible by 56.
Can a shipment of 448 items be divided into packages of 56 items each without leftovers?
Yes, 448 is divisible by 56.
Check the divisibility of 448 by 8 and 7.
1) For 8: The last three digits are 448, and 448 ÷ 8 = 56, so it's divisible by 8.
2) For 7: Multiply the last digit by 2, 8 × 2 = 16. Subtract from the rest, 44 – 16 = 28.
3) Since 28 is a multiple of 7, 448 is divisible by 7.
4) Thus, 448 is divisible by both 8 and 7, making it divisible by 56.
A concert venue has 300 seats. Can they arrange the seats into blocks of 56?
No, 300 is not divisible by 56.
Check divisibility by 8 and 7.
1) For 8: The last three digits are 300, and 300 ÷ 8 = 37.5, which is not an integer, so it's not divisible by 8.
2) Without needing to check further, since 300 is not divisible by 8, it cannot be divisible by 56.
A farmer has 560 apples. Can he distribute them equally in baskets of 56 apples each?
Yes, 560 is divisible by 56.
Verify divisibility by 8 and 7.
1) For 8: The last three digits are 560, and 560 ÷ 8 = 70, so it is divisible by 8.
2) For 7: Multiply the last digit by 2, 0 × 2 = 0. Subtract from the rest, 56 – 0 = 56.
3) Since 56 is a multiple of 7, 560 is divisible by 7.
4) Therefore, 560 is divisible by both 8 and 7, confirming it is divisible by 56.
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.