5,746 and 3,240 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 prime factorization:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
5,746 = 2 × 132 × 17
5,746 is not a prime number, is a composite one.
3,240 = 23 × 34 × 5
3,240 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).
Step 1. Divide the larger number by the smaller one:
5,746 ÷ 3,240 = 1 + 2,506
Step 2. Divide the smaller number by the above operation's remainder:
3,240 ÷ 2,506 = 1 + 734
Step 3. Divide the remainder of the step 1 by the remainder of the step 2:
2,506 ÷ 734 = 3 + 304
Step 4. Divide the remainder of the step 2 by the remainder of the step 3:
734 ÷ 304 = 2 + 126
Step 5. Divide the remainder of the step 3 by the remainder of the step 4:
304 ÷ 126 = 2 + 52
Step 6. Divide the remainder of the step 4 by the remainder of the step 5:
126 ÷ 52 = 2 + 22
Step 7. Divide the remainder of the step 5 by the remainder of the step 6:
52 ÷ 22 = 2 + 8
Step 8. Divide the remainder of the step 6 by the remainder of the step 7:
22 ÷ 8 = 2 + 6
Step 9. Divide the remainder of the step 7 by the remainder of the step 8:
8 ÷ 6 = 1 + 2
Step 10. Divide the remainder of the step 8 by the remainder of the step 9:
6 ÷ 2 = 3 + 0
At this step, the remainder is zero, so we stop:
2 is the number we were looking for - the last non-zero remainder.
This is the greatest (highest) common factor (divisor).
gcf (hcf, gcd) (5,746; 3,240) = 2 ≠ 1
Coprime numbers (prime to each other, relatively prime) (5,746; 3,240)? No.
gcf (hcf, gcd) (3,240; 5,746) = 2 ≠ 1