Coprime numbers, prime to each other, relatively prime: 16 and 46,288?

16 and 46,288: coprime numbers?

16 and 46,288 are not coprime (relatively, mutually prime) if they have common prime factors, that is, if their greatest (highest) common factor (divisor), gcf, hcf, gcd, is not 1.

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

Approach 1. Integer numbers divisibility:

Divide the larger number by the smaller one.


Notice that dividing our numbers leaves no remainder:


46,288 ÷ 16 = 2,893 + 0;


So, 46,288 = 16 × 2,893;


So, 46,288 is divisible by 16;


16 is a factor (a divisor) of 46,288;


Consequently, gcf, hcf, gcd (16; 46,288) = 16.


Coprime numbers (relatively prime) (16; 46,288)? No.
gcf, hcf, gcd (16; 46,288) = 16.

Approach 2. Integer numbers prime factorization:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


16 = 24;
16 is not a prime, is a composite number;


46,288 = 24 × 11 × 263;
46,288 is not a prime, is a composite number;


Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.


A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.


>> Integer numbers prime factorization


Calculate greatest (highest) common factor (divisor):

Multiply all the common prime factors, by the lowest exponents (if any).


gcf, hcf, gcd (16; 46,288) = 24 = 16;



Coprime numbers (relatively prime) (16; 46,288)? No.
46,288 has all the prime factors of the number 16.
gcf, hcf, gcd (16; 46,288) = 16.

Final answer:

16 and 46,288 are not coprime (relatively, mutually prime) if they have common prime factors, that is, if their greatest (highest) common factor (divisor), gcf, hcf, gcd, is not 1.
Coprime numbers (relatively prime) (16; 46,288)? No.
gcf, hcf, gcd (16; 46,288) = 16.

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Coprime numbers (numbers prime to each other, relatively prime, mutually prime)

Integers "a" and "b" are said to be relatively prime, mutually prime, or coprime if the only positive integer that divides both of them is 1. This is equivalent to their only common positive factor being 1. This is also equivalent to their greatest common factor (divisor) being 1.

For example, 16 and 17 are coprime, being commonly divisible by only 1, but 16 and 24 are not, because they are both divisible by 8. The numbers 1 and -1 are the only integers coprime to every integer, and they are the only integers to be coprime with 0. A fast way to determine whether two numbers are coprime is given by the Euclidean algorithm: Euclid's algorithm


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