Is 38 Divisible by 7 or 8?
Determining whether 38 is divisible by 7 or 8 involves simple division and understanding divisibility rules. The number 38 is not divisible by either 7 or 8, as neither division results in a whole number. Let’s explore the details and methods for checking divisibility.
How to Check Divisibility by 7?
Checking if a number is divisible by 7 can be slightly more complex than other divisibility rules. Here’s a step-by-step method:
- Double the Last Digit: Take the last digit of the number and double it.
- Subtract from the Rest: Subtract this doubled value from the rest of the number.
- Check the Result: If the result is divisible by 7, then the original number is divisible by 7.
Example for 38
- Last Digit: 8
- Double It: 8 × 2 = 16
- Subtract: 3 – 16 = -13
Since -13 is not divisible by 7, 38 is not divisible by 7.
How to Check Divisibility by 8?
To determine if a number is divisible by 8, you only need to consider the last three digits of the number. For numbers with fewer than three digits, you simply use the entire number.
Example for 38
- Since 38 has fewer than three digits, use the entire number.
- Divide: 38 ÷ 8 = 4.75
Since 4.75 is not a whole number, 38 is not divisible by 8.
Divisibility Rules for Quick Reference
Here’s a quick guide to divisibility rules for other common numbers:
- 2: A number is divisible by 2 if it is even.
- 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- 4: A number is divisible by 4 if the last two digits form a number divisible by 4.
- 5: A number is divisible by 5 if it ends in 0 or 5.
- 6: A number is divisible by 6 if it is divisible by both 2 and 3.
Practical Examples of Divisibility
Understanding divisibility is crucial in many mathematical and real-world applications, such as simplifying fractions or determining factors. For instance, knowing that 38 is not divisible by either 7 or 8 can help in solving equations or performing calculations more efficiently.
People Also Ask
What are the factors of 38?
The factors of 38 are numbers that divide 38 exactly without leaving a remainder. The factors are 1, 2, 19, and 38. These include both 1 and 38 itself, as well as the prime factors 2 and 19.
Is 38 a prime number?
No, 38 is not a prime number. A prime number has only two factors: 1 and itself. Since 38 has additional factors (2 and 19), it is not considered a prime number.
How do you find the greatest common divisor (GCD) of 38?
To find the greatest common divisor of 38 and another number, list all factors of both numbers and identify the largest factor they have in common. For example, the GCD of 38 and 76 is 38, since 38 is a factor of 76.
What is the prime factorization of 38?
The prime factorization of 38 is 2 × 19. This means that 38 can be expressed as the product of the prime numbers 2 and 19.
Can 38 be divided evenly by any other numbers?
Yes, besides 1 and 38, the number 38 can be evenly divided by 2 and 19, as these are its factors.
Summary
In summary, 38 is not divisible by 7 or 8, as confirmed through the application of divisibility rules. Understanding these rules provides valuable insights into number properties and aids in various mathematical computations. For further exploration, consider learning about the divisibility rules for other numbers, such as 9 and 11, to enhance your numerical proficiency.
