Last updated on May 26th, 2025
The divisibility rule is a way to determine whether a number is divisible by another number without performing the actual division. In real life, we can use divisibility rules for quick calculations, evenly distributing items, and organizing data. In this topic, we will learn about the divisibility rule of 350.
The divisibility rule for 350 is a method by which we can determine if a number is divisible by 350 without performing division. To check whether a number, say 2450, is divisible by 350, we can use the following steps:
Step 1: Check if the number is divisible by 2, 5, and 7, as 350 = 2 × 5 × 7.
Step 2: For divisibility by 2, the last digit of the number should be even. In 2450, the last digit is 0, which is even.
Step 3: For divisibility by 5, the last digit should be 0 or 5. In 2450, the last digit is 0.
Step 4: For divisibility by 7, there are several methods, but one of the simplest is to divide the number by 7 directly or use a known divisibility rule for 7. For 2450, dividing by 7 gives a whole number (350).
Since 2450 is divisible by 2, 5, and 7, it is therefore divisible by 350.
Learning divisibility rules can help students master division. Let’s explore a few tips and tricks for the divisibility rule of 350.
Recognize that 350 is the product of 2, 5, and 7. Check divisibility by each of these numbers to determine divisibility by 350.
Familiarize yourself with the divisibility rules for 2, 5, and 7 individually to quickly evaluate divisibility by 350.
If a number is large, break it down and check divisibility by each factor separately.
Knowing multiples of 350, such as 350, 700, 1050, can help quickly identify divisible numbers.
Use the division method to verify and confirm the results of the divisibility rule.
The divisibility rule of 350 helps quickly determine if a given number is divisible by 350, but mistakes can lead to incorrect results. Here are some common mistakes and how to avoid them.
Is 2450 divisible by 350?
Yes, 2450 is divisible by 350.
To determine if 2450 is divisible by 350, check the divisibility by both 2, 5, and 7:
1) The number ends in 0, so it is divisible by both 2 and 5.
2) Sum the digits of the number: 2 + 4 + 5 + 0 = 11. This is not directly divisible by 7, but we perform the divisibility check by subtracting twice the last digit from the rest: 245 - 0 = 245, and then 24 - 10 = 14. Since 14 is a multiple of 7, 2450 is divisible by 350.
Check the divisibility rule of 350 for 7000.
Yes, 7000 is divisible by 350.
For 7000 to be divisible by 350, it must be divisible by 2, 5, and 7:
1) The number ends in 0, so it is divisible by both 2 and 5.
2) For divisibility by 7, subtract twice the last digit from the rest: 700 - 0 = 700, and then 70 - 0 = 70. Since 70 is a multiple of 7, 7000 is divisible by 350.
Is 490 divisible by 350?
No, 490 is not divisible by 350.
To check if 490 is divisible by 350, it must be divisible by 2, 5, and 7:
1) The number ends in 0, making it divisible by both 2 and 5.
2) For divisibility by 7, subtract twice the last digit from the rest: 49 - 0 = 49. Since 49 is a multiple of 7, 490 meets the divisibility criteria for 7.
However, since 490 is not the result of multiplying 350 by an integer, it is not divisible by 350.
Can 28000 be divisible by 350 following the divisibility rule?
Yes, 28000 is divisible by 350.
To verify if 28000 is divisible by 350, ensure it is divisible by 2, 5, and 7:
1) It ends in 0, meaning it is divisible by both 2 and 5.
2) For divisibility by 7, subtract twice the last digit from the rest: 2800 - 0 = 2800, and then 280 - 0 = 280. Since 280 is a multiple of 7, 28000 is divisible by 350.
Is 175 divisible by 350?
No, 175 is not divisible by 350.
To determine if 175 is divisible by 350, it must satisfy divisibility by 2, 5, and 7:
1) The number ends in 5, so it is only divisible by 5.
2) 175 is not divisible by 2 since it does not end in an even number.
3) For divisibility by 7, subtract twice the last digit from the rest: 17 - 10 = 7. While 7 is a multiple of 7, since 175 does not meet the criteria for divisibility by 2 and is not the result of multiplying 350 by an integer, it is not divisible by 350.
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.