Are the two numbers 5,886 and 8,841 coprime (relatively prime, prime to each other)? Check if their greatest common factor, gcf, is equal to 1

Are 5,886 and 8,841 coprime (prime to each other, relatively prime)?

5,886 and 8,841 are not relatively prime - if there is at least one number other than 1 that evenly divides the two numbers (without a remainder) - or, in other words - if their greatest (highest) common factor (divisor), gcf (hcf, gcd), is not 1.

Calculate the greatest (highest) common factor (divisor), gcf (hcf, gcd), of the numbers

Method 1. The prime factorization:

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


5,886 = 2 × 33 × 109
5,886 is not a prime number, is a composite one.


8,841 = 3 × 7 × 421
8,841 is not a prime number, is a composite one.


The numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has only 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 numbers


Calculate the greatest (highest) common factor (divisor), gcf (hcf, gcd):

Multiply all the common prime factors of the two numbers, taken by their smallest exponents (powers).


gcf (hcf, gcd) (5,886; 8,841) = 3



Coprime numbers (prime to each other, relatively prime) (5,886; 8,841)? No.
The two numbers have common prime factors.
gcf (hcf, gcd) (5,886; 8,841) = 3

Method 2. The Euclidean Algorithm:

This algorithm involves the process of dividing numbers and calculating the remainders.


'a' and 'b' are the two natural numbers, 'a' >= 'b'.


Divide 'a' by 'b' and get the remainder of the operation, 'r'.


If 'r' = 0, STOP. 'b' = the gcf (hcf, gcd) of 'a' and 'b'.


Else: Replace ('a' by 'b') and ('b' by 'r'). Return to the step above.



Step 1. Divide the larger number by the smaller one:
8,841 ÷ 5,886 = 1 + 2,955
Step 2. Divide the smaller number by the above operation's remainder:
5,886 ÷ 2,955 = 1 + 2,931
Step 3. Divide the remainder of the step 1 by the remainder of the step 2:
2,955 ÷ 2,931 = 1 + 24
Step 4. Divide the remainder of the step 2 by the remainder of the step 3:
2,931 ÷ 24 = 122 + 3
Step 5. Divide the remainder of the step 3 by the remainder of the step 4:
24 ÷ 3 = 8 + 0
At this step, the remainder is zero, so we stop:
3 is the number we were looking for - the last non-zero remainder.
This is the greatest (highest) common factor (divisor).


gcf (hcf, gcd) (5,886; 8,841) = 3


>> The Euclidean Algorithm

Coprime numbers (prime to each other, relatively prime) (5,886; 8,841)? No.
gcf (hcf, gcd) (5,886; 8,841) = 3


The final answer:
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5,886 and 8,841 are not relatively prime - if there is at least one number other than 1 that evenly divides the two numbers (without a remainder) - or, in other words - if their greatest (highest) common factor (divisor), gcf (hcf, gcd), is not 1.
Coprime numbers (prime to each other, relatively prime) (5,886; 8,841)? No.
gcf (hcf, gcd) (5,886; 8,841) = 3

The latest 5 pairs of numbers that have been checked on whether they are coprime (prime to each other, relatively prime) or not

Are the two numbers coprime (relatively prime)?

Two natural numbers are coprime (relatively prime, prime to each other) - if there is no number that is evenly dividing both numbers (= without a remainder), that is, if their greatest (highest) common factor (divisor), gcf, or hcf, or gcd is 1.

Two natural numbers are not relatively prime - if there is at least one number that evenly divides the two numbers, that is, if their greatest common factor, gcf, is not 1.

Coprime numbers (also called: numbers prime to each other, relatively prime, mutually prime)


What is a prime number? Definition, examples

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

Completely reduce (simplify) fractions to the lowest terms: Steps and Examples