999,999,999,980 and 999,999,999,978 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.
999,999,999,980 = 22 × 5 × 29 × 1,724,137,931
999,999,999,980 is not a prime number, is a composite one.
999,999,999,978 = 2 × 3 × 7 × 59 × 67 × 6,023,153
999,999,999,978 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) (999,999,999,980; 999,999,999,978) = 2 ≠ 1
Coprime numbers (prime to each other, relatively prime) (999,999,999,980; 999,999,999,978)? No.
The two numbers have common prime factors.
gcf (hcf, gcd) (999,999,999,978; 999,999,999,980) = 2 ≠ 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:
999,999,999,980 ÷ 999,999,999,978 = 1 + 2
Step 2. Divide the smaller number by the above operation's remainder:
999,999,999,978 ÷ 2 = 499,999,999,989 + 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) (999,999,999,980; 999,999,999,978) = 2 ≠ 1
Coprime numbers (prime to each other, relatively prime) (999,999,999,980; 999,999,999,978)? No.
gcf (hcf, gcd) (999,999,999,978; 999,999,999,980) = 2 ≠ 1