Are the two numbers 29,988 and 7,197,120 coprime (relatively prime, prime to each other)? Check if their greatest common factor, gcf, is equal to 1

Are 29,988 and 7,197,120 coprime (prime to each other, relatively prime)?

29,988 and 7,197,120 are not relatively prime -- if there is at least one number 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 divisibility of numbers:

Divide the larger number by the smaller one.


When dividing the two numbers, there is no remainder:


7,197,120 ÷ 29,988 = 240 + 0


=> 7,197,120 = 29,988 × 240


=> 7,197,120 is divisible by 29,988.


=> 29,988 is a factor (a divisor) of 7,197,120;


Consequently, gcf (hcf, gcd) (29,988; 7,197,120) = 29,988


Coprime numbers (prime to each other, relatively prime) (29,988; 7,197,120)? No.
gcf (hcf, gcd) (29,988; 7,197,120) = 29,988

Method 2. The prime factorization:

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


29,988 = 22 × 32 × 72 × 17
29,988 is not a prime number, is a composite one.


7,197,120 = 26 × 33 × 5 × 72 × 17
7,197,120 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) (29,988; 7,197,120) = 22 × 32 × 72 × 17 = 29,988



Coprime numbers (prime to each other, relatively prime) (29,988; 7,197,120)? No.
7,197,120 has all the prime factors of the number 29,988.
gcf (hcf, gcd) (29,988; 7,197,120) = 29,988

The final answer:

29,988 and 7,197,120 are not relatively prime -- if there is at least one number 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) (29,988; 7,197,120)? No.
gcf (hcf, gcd) (29,988; 7,197,120) = 29,988

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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.

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