# Are the Two Numbers 2,240 and 5,637 Coprime (Relatively Prime, Prime to Each Other)? Check if Their Greatest Common Factor, GCF, Is Equal to 1. Online Calculator

## Are the numbers 2,240 and 5,637 coprime (prime to each other, relatively prime)?

### 2,240 and 5,637 are coprime (relatively prime)... if:

#### If there is no number other than 1 that evenly divides (without a remainder) both numbers. Or...

#### Or, in other words, if their greatest (highest) common factor (divisor), gcf (hcf, gcd), is equal to 1.

## Calculate the greatest (highest) common factor (divisor),

gcf (hcf, gcd), of the two numbers

### Method 1. The prime factorization:

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

#### 2,240 = 2^{6} × 5 × 7

2,240 is not a prime number, is a composite one.

#### 5,637 = 3 × 1,879

5,637 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).

#### But the numbers have no common prime factors.

### gcf (hcf, gcd) (2,240; 5,637) = 1

Coprime numbers (prime to each other, relatively prime)

## Coprime numbers (prime to each other, relatively prime) (2,240; 5,637)? Yes.

The numbers have no common prime factors.

gcf (hcf, gcd) (2,240; 5,637) = 1

Scroll down for the 2nd method...

### Method 2. The Euclidean Algorithm:

#### This algorithm involves the process of dividing numbers and calculating the remainders.

#### 'a' and 'b' are the two natural numbers, 'a' >= 'b'.

#### Divide 'a' by 'b' and get the remainder of the operation, 'r'.

#### If 'r' = 0, STOP. 'b' = the gcf (hcf, gcd) of 'a' and 'b'.

#### Else: Replace ('a' by 'b') and ('b' by 'r'). Return to the step above.

#### Step 1. Divide the larger number by the smaller one:

5,637 ÷ 2,240 = 2 + 1,157

Step 2. Divide the smaller number by the above operation's remainder:

2,240 ÷ 1,157 = 1 + 1,083

Step 3. Divide the remainder of the step 1 by the remainder of the step 2:

1,157 ÷ 1,083 = 1 + 74

Step 4. Divide the remainder of the step 2 by the remainder of the step 3:

1,083 ÷ 74 = 14 + 47

Step 5. Divide the remainder of the step 3 by the remainder of the step 4:

74 ÷ 47 = 1 + 27

Step 6. Divide the remainder of the step 4 by the remainder of the step 5:

47 ÷ 27 = 1 + 20

Step 7. Divide the remainder of the step 5 by the remainder of the step 6:

27 ÷ 20 = 1 + 7

Step 8. Divide the remainder of the step 6 by the remainder of the step 7:

20 ÷ 7 = 2 + 6

Step 9. Divide the remainder of the step 7 by the remainder of the step 8:

7 ÷ 6 = 1 + 1

Step 10. Divide the remainder of the step 8 by the remainder of the step 9:

6 ÷ 1 = 6 + 0

At this step, the remainder is zero, so we stop:

1 is the number we were looking for - the last non-zero remainder.

This is the greatest (highest) common factor (divisor).

### gcf (hcf, gcd) (2,240; 5,637) = 1

## Coprime numbers (prime to each other, relatively prime) (2,240; 5,637)? Yes.

gcf (hcf, gcd) (2,240; 5,637) = 1

### Other similar operations with coprime numbers: