Are the two numbers 688 and 550,400 coprime (relatively prime, prime to each other)? Check if their greatest common factor, gcf, is equal to 1

Are 688 and 550,400 coprime (prime to each other, relatively prime)?

688 and 550,400 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:

550,400 ÷ 688 = 800 + 0

=> 550,400 = 688 × 800

=> 550,400 is divisible by 688.

=> 688 is a factor (a divisor) of 550,400;

Consequently, gcf (hcf, gcd) (688; 550,400) = 688

Coprime numbers (prime to each other, relatively prime) (688; 550,400)? No.
gcf (hcf, gcd) (688; 550,400) = 688

Method 2. The prime factorization:

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

688 = 2⁴ × 43
688 is not a prime number, is a composite one.

550,400 = 2⁹ × 5² × 43
550,400 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) (688; 550,400) = 2⁴ × 43 = 688

Coprime numbers (prime to each other, relatively prime) (688; 550,400)? No.
550,400 has all the prime factors of the number 688.
gcf (hcf, gcd) (688; 550,400) = 688

The final answer:

688 and 550,400 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) (688; 550,400)? No.
gcf (hcf, gcd) (688; 550,400) = 688

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

The number "a" and "b" are said to be relatively prime, mutually prime, or coprime if the only positive integer that evenly divides both of them is 1.
The coprime numbers are pairs of (at least two) numbers that do not have any other common factor than 1.
When the only common factor is 1, then this is also equivalent to their greatest (highest) common factor (divisor) being 1.

Examples of pairs of coprime numbers:
The coprime numbers are not necessarily prime numbers themselves, for example 4 and 9 - these two numbers are not prime, they are composite numbers, since 4 = 2 × 2 = 2² and 9 = 3 × 3 = 3². But the gcf (4, 9) = 1, so they are coprime, or prime to each other, or relatively prime.
Sometimes, the coprime numbers in a pair are prime numbers themselves, for example (3 and 5), or (7 and 11), (13 and 23).
Some other times, the numbers that are prime to each other may or may not be prime, for example (5 and 6), (7 and 12), (15 and 23).

Examples of pairs of numbers that are not coprime:
16 and 24 are not coprime, since they are both divisible by 1, 2, 4 and 8 (1, 2, 4 and 8 are their common factors).
6 and 10 are not coprime, since they are both divisible by 1 and 2.

Some properties of the coprime numbers:
The greatest (highest) common factor (divisor) of two coprime numbers is always 1.
The least common multiple, LCM, of two coprimes is always their product: LCM (a, b) = a × b.
The numbers 1 and -1 are the only integers coprime to every integer, for example (1 and 2), (1 and 3), (1 and 4), (1 and 5), (1 and 6), and so on, are pairs of coprime numbers since their greatest (highest) common factor (divisor) is 1.
The numbers 1 and -1 are the only integers coprime to 0.
Any two prime numbers are always coprime, for example (2 and 3), (3 and 5), (5 and 7) and so on.
Any two consecutive numbers are co-prime, for example (1 and 2), (2 and 3), (3 and 4), (4 and 5), (5 and 6), (6 and 7), (7 and 8), (8 and 9), (9 and 10), and so on.
The sum of two coprime numbers, a + b, is always relatively prime to their product, a × b. For example, 7 and 10 are coprime numbers, 7 + 10 = 17 is relatively prime to 7 × 10 = 70. Another example, 9 and 11 are coprime, and their sum, 9 + 11 = 20 is relatively prime to their product, 9 × 11 = 99.
A quick way to determine whether two numbers are prime to each other is given by the Euclidean algorithm: The Euclidean Algorithm

Are the two numbers 688 and 550,400 coprime (relatively prime, prime to each other)? Check if their greatest common factor, gcf, is equal to 1

Are 688 and 550,400 coprime (prime to each other, relatively prime)?

688 and 550,400 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:

550,400 ÷ 688 = 800 + 0

=> 550,400 = 688 × 800

=> 550,400 is divisible by 688.

=> 688 is a factor (a divisor) of 550,400;

Consequently, gcf (hcf, gcd) (688; 550,400) = 688

Coprime numbers (prime to each other, relatively prime) (688; 550,400)? No. gcf (hcf, gcd) (688; 550,400) = 688

Method 2. The prime factorization:

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

688 = 24 × 43 688 is not a prime number, is a composite one.

550,400 = 29 × 52 × 43 550,400 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.

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) (688; 550,400) = 24 × 43 = 688

Coprime numbers (prime to each other, relatively prime) (688; 550,400)? No. 550,400 has all the prime factors of the number 688. gcf (hcf, gcd) (688; 550,400) = 688

The final answer:

More operations of this kind:

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.

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

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

Coprime numbers (prime to each other, relatively prime) (688; 550,400)? No.
gcf (hcf, gcd) (688; 550,400) = 688

688 = 2⁴ × 43
688 is not a prime number, is a composite one.

550,400 = 2⁹ × 5² × 43
550,400 is not a prime number, is a composite one.

gcf (hcf, gcd) (688; 550,400) = 2⁴ × 43 = 688

Coprime numbers (prime to each other, relatively prime) (688; 550,400)? No.
550,400 has all the prime factors of the number 688.
gcf (hcf, gcd) (688; 550,400) = 688