The GCF (121 and 605) = ? Calculate the Greatest (Highest) Common Factor (Divisor), GCF (HCF, GCD), of the Numbers, by Two Methods: 1) The Numbers' Divisibility and 2) The Prime Factorization
gcf, hcf, gcd (121; 605) = ?
Method 1. The divisibility of numbers:
Divide the larger number by the smaller one.
Note that when the numbers are divided, the remainder is zero:
605 ÷ 121 = 5 + 0
⇒ 605 = 121 × 5
So, 605 is divisible by 121.
And 121 is a factor (divisor) of 605.
Also, the greatest factor (divisor) of 121 is the number itself, 121.
The greatest (highest) common factor (divisor),
gcf, hcf, gcd (121; 605) = 121 = 112
605 is divisible by 121
Scroll down for the 2nd method...
Method 2. The prime factorization:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
121 = 112
121 is not a prime number but a composite one.
605 = 5 × 112
605 is not a prime number but a composite one.
* Prime number: a natural number that is only divisible by 1 and itself. A prime number has exactly 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):
Multiply all the common prime factors, taken by their smallest exponents (the smallest powers).
The greatest (highest) common factor (divisor),
gcf, hcf, gcd (121; 605) = 112 = 121
605 contains all the prime factors of the number 121
605 is divisible by 121.
Why do we need to calculate the greatest common factor?
Once you've calculated the greatest common factor of the numerator and the denominator of a fraction, it becomes much easier to fully reduce (simplify) the fraction to the lowest terms (the smallest possible numerator and denominator).
Other similar operations with the greatest (highest) common factor (divisor):
Calculator of the greatest (highest) common factor (divisor), gcf, hcf, gcd
Calculate the greatest (highest) common factor (divisor) of numbers, gcd, hcf, gcd:
Method 1: Run the prime factorization of the numbers - then multiply all the common prime factors, taken by their smallest exponents. If there are no common prime factors, then gcf equals 1.
Method 2: The Euclidean Algorithm.
Method 3: The divisibility of the numbers.