Are the Two Numbers 345,720 and 6,997,372,800 Coprime (Relatively Prime, Prime to Each Other)? Check if Their Greatest Common Factor, GCF, Is Equal to 1
Are the numbers 345,720 and 6,997,372,800 coprime (prime to each other, relatively prime)?
345,720 and 6,997,372,800 are not relatively prime... if:
If there is at least one number other than 1 that evenly divides the two numbers (without a remainder). Or...
Or, in other words, if their greatest (highest) common factor (divisor), gcf (hcf, gcd), is not equal to 1.
Calculate the greatest (highest) common factor (divisor),
gcf (hcf, gcd), of the two numbers
Method 1. The divisibility of numbers:
Divide the larger number by the smaller one.
When dividing the two numbers, there is no remainder:
6,997,372,800 ÷ 345,720 = 20,240 + 0
⇒ 6,997,372,800 = 345,720 × 20,240
⇒ 6,997,372,800 is divisible by 345,720
⇒ 345,720 is a factor (a divisor) of 6,997,372,800
Consequently, gcf (hcf, gcd) (345,720; 6,997,372,800) = 345,720 ≠ 1
Coprime numbers (prime to each other, relatively prime) (345,720; 6,997,372,800)? No.
gcf (hcf, gcd) (345,720; 6,997,372,800) = 345,720 ≠ 1
Scroll down for the 2nd method...
Method 2. The prime factorization:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
345,720 = 23 × 3 × 5 × 43 × 67
345,720 is not a prime number, is a composite one.
6,997,372,800 = 27 × 3 × 52 × 11 × 23 × 43 × 67
6,997,372,800 is not a prime number, is a composite one.
Prime number: a number that is divisible (dividing evenly) only by 1 and itself. A prime number has only two factors: 1 and itself.
Composite number: a natural number that has at least one other factor than 1 and itself.
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) (345,720; 6,997,372,800) = 23 × 3 × 5 × 43 × 67 = 345,720 ≠ 1
Coprime numbers (prime to each other, relatively prime) (345,720; 6,997,372,800)? No.
6,997,372,800 has all the prime factors of the number 345,720.
gcf (hcf, gcd) (345,720; 6,997,372,800) = 345,720 ≠ 1
Other similar operations with coprime numbers:
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.