88 and 8,605 are coprime (relatively prime) -- if there is no number that evenly divides the both numbers (without a remainder) -- that is -- if their greatest (highest) common factor (divisor), gcf (hcf, gcd), is 1.
Calculate the greatest (highest) common factor (divisor), gcf (hcf, gcd), of the numbers
Method 1. The prime factorization:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
88 = 23 × 11
88 is not a prime number, is a composite one.
8,605 = 5 × 1,721
8,605 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).
But the numbers have no common prime factors.
gcf (hcf, gcd) (88; 8,605) = 1
Coprime numbers (prime to each other, relatively prime)
Coprime numbers (prime to each other, relatively prime) (88; 8,605)? Yes.
The numbers have no common prime factors.
gcf (hcf, gcd) (88; 8,605) = 1
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:
8,605 ÷ 88 = 97 + 69
Step 2. Divide the smaller number by the above operation's remainder:
88 ÷ 69 = 1 + 19
Step 3. Divide the remainder of the step 1 by the remainder of the step 2:
69 ÷ 19 = 3 + 12
Step 4. Divide the remainder of the step 2 by the remainder of the step 3:
19 ÷ 12 = 1 + 7
Step 5. Divide the remainder of the step 3 by the remainder of the step 4:
12 ÷ 7 = 1 + 5
Step 6. Divide the remainder of the step 4 by the remainder of the step 5:
7 ÷ 5 = 1 + 2
Step 7. Divide the remainder of the step 5 by the remainder of the step 6:
5 ÷ 2 = 2 + 1
Step 8. Divide the remainder of the step 6 by the remainder of the step 7:
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) (88; 8,605) = 1
Coprime numbers (prime to each other, relatively prime) (88; 8,605)? Yes.
gcf (hcf, gcd) (88; 8,605) = 1