Is the number 2,194 divisible by 273? Can the first number be divided evenly by the second (without a remainder)? Compare the prime factorizations of the two numbers

Is the number 2,194 divisible by 273?

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.


2,194 would be divisible by 273 only if there was a natural number 'n', so that:
2,194 = 'n' × 273


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


2,194 ÷ 273 = 8 + remainder 10


There is no natural number 'n' such that: 2,194 = 'n' × 273.


The number 2,194 is not divisible by 273.


Note:

1) If you subtract the remainder of the above operation from the original number, 2,194, then the result is a number that is divisible by the second number, 273:


2,194 - 10 = 2,184


2,184 = 8 × 273


2) If you subtract the remainder of the above operation from the second number, 273, and then add the result to the original number, 2,194, you get a number that is divisible by the second number:

273 - 10 = 263


2,194 + 263 = 2,457.


2,457 = 9 × 273.


The number 2,194 is not divisible by 273
When the two numbers are divided, there is a remainder.

Method 2. The prime factorization of the numbers:

When are two numbers divisible?

The number 2,194 would be divisible by 273 only if its prime factorization contained all the prime factors that appear in the prime factorization of the number 273.


The prime factorization of the numbers:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.


2,194 = 2 × 1,097
2,194 is not a prime number but a composite one.


273 = 3 × 7 × 13
273 is not a prime number but a composite one.



* The natural numbers that are only divisible 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 prime factorization of the number 2,194 does not contain (all) the prime factors that occur in the prime factorization of 273.


The number 2,194 is not divisible by 273.


The number 2,194 is not divisible by 273.


The final answer:
(scroll down)

The number 2,194 is not divisible by 273.
When the two numbers are divided, there is a remainder.
The prime factorization of the number 2,194 does not contain (all) the prime factors that occur in the prime factorization of 273.

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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).

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