Is the number 39,421 divisible by 8,215? Can the first number be divided evenly by the second (without a remainder)? Compare the prime factorizations of the two numbers

Is the number 39,421 divisible by 8,215?

Method 1. The division of the two numbers:

A natural number 'A' could only be divisible by another number 'B' if after dividing 'A' by 'B' the remainder was zero.


39,421 would be divisible by 8,215 only if there was a natural number 'n', so that:
39,421 = 'n' × 8,215


When we divide the two numbers, there is a remainder:


39,421 ÷ 8,215 = 4 + remainder 6,561


There is no natural number 'n' such that: 39,421 = 'n' × 8,215.


The number 39,421 is not divisible by 8,215.


Note:

1) If you subtract the remainder of the above operation from the original number, 39,421, then the result is a number that is divisible by the second number, 8,215:


39,421 - 6,561 = 32,860


32,860 = 4 × 8,215


The article continues below...


2) If you subtract the remainder of the above operation from the second number, 8,215, and then add the result to the original number, 39,421, you get a number that is divisible by the second number:

8,215 - 6,561 = 1,654


39,421 + 1,654 = 41,075.


41,075 = 5 × 8,215.


The number 39,421 is not divisible by 8,215
When the two numbers are divided, there is a remainder.
Scroll down for the 2nd method...

Method 2. The prime factorization of the numbers

When are two numbers divisible?

The number 39,421 would be divisible by 8,215 only if its prime factorization (the decomposition into prime factors) contained all the prime factors that appear in the prime factorization of the number 8,215.


The prime factorization of the numbers:

The prime factorization of a number (the decomposition into prime factors): finding the prime numbers that multiply together to make that number.


39,421 = 79 × 499
39,421 is not a prime number but a composite one.


8,215 = 5 × 31 × 53
8,215 is not a prime number but a composite one.



* The natural numbers that are divisible only by 1 and themselves are called prime numbers. A prime number has exactly two factors: 1 and itself.
* A composite number is a natural number that has at least one other factor than 1 and itself.


The final answer:
The number 39,421 is not divisible by 8,215.

The prime factorization of the number 39,421 does not contain (all) the prime factors that occur in the prime factorization of 8,215.
When the two numbers are divided, there is a remainder.

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Calculator: Are the two numbers divisible?

The divisibility of the natural numbers:

Method 1: Divide the numbers and check the remainder of the operation. If the remainder is zero, then the numbers are divisible.

Method 2: The prime factorization of the numbers (the decomposition of the numbers into prime factors).

1. What is the numbers' divisibility? 2. Divisibility rules. 3. Calculating the divisors (factors). 4. Quick ways to determine whether a number is divisible by another one or not.

Some articles on the prime numbers

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What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

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