Coprime numbers, prime to each other, relatively prime: 528 and 88?

528 and 88 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 (7,093; 88)? ... (528; 8,615)?

Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd.
Two methods used below.

Approach 1. Integer numbers divisibility:

Divide the larger number by the smaller one.


Notice that dividing our numbers leaves no remainder:


528 ÷ 88 = 6 + 0;


So, 528 = 88 × 6;


So, 528 is divisible by 88;


88 is a factor (a divisor) of 528;


Consequently, gcf, hcf, gcd (88; 528) = 88.


Note that this is also the first step of the Euclidean Algorithm, where the division of the numbers stops when a remainder equal to zero is reported.


Coprime numbers (relatively prime) (88; 528)? No.
gcf, hcf, gcd (88; 528) = 88.

>> Integer numbers divisibility


Approach 2. Integer numbers prime factorization:

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


528 = 24 × 3 × 11;
528 is not a prime, is a composite number;


88 = 23 × 11;
88 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.


Calculate greatest (highest) common factor (divisor):

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


gcf, hcf, gcd (528; 88) = 23 × 11 = 88;



Coprime numbers (relatively prime) (528; 88)? No.
528 has all the prime factors of the number 88.
gcf, hcf, gcd (88; 528) = 88.

>> Integer numbers prime factorization


Final answer:

528 and 88 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) (528; 88)? No.
gcf, hcf, gcd (528; 88) = 88.

More operations of this kind:

coprime (7,093; 88)? ... (528; 8,615)?

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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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