311 and 5,154 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.
311 is a prime number, it cannot be prime factorized.
5,154 = 2 × 3 × 859
5,154 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:
5,154 ÷ 311 = 16 + 178
Step 2. Divide the smaller number by the above operation's remainder:
311 ÷ 178 = 1 + 133
Step 3. Divide the remainder of the step 1 by the remainder of the step 2:
178 ÷ 133 = 1 + 45
Step 4. Divide the remainder of the step 2 by the remainder of the step 3:
133 ÷ 45 = 2 + 43
Step 5. Divide the remainder of the step 3 by the remainder of the step 4:
45 ÷ 43 = 1 + 2
Step 6. Divide the remainder of the step 4 by the remainder of the step 5:
43 ÷ 2 = 21 + 1
Step 7. Divide the remainder of the step 5 by the remainder of the step 6:
2 ÷ 1 = 2 + 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) (311; 5,154) = 1
Are the numbers 311 and 5,154 coprime (prime to each other, relatively prime)? Yes, they are.
gcf (hcf, gcd) (311; 5,154) = 1