The GCF (7 and 9,849) = ? 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 (7; 9,849) = ?
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:
9,849 ÷ 7 = 1,407 + 0
⇒ 9,849 = 7 × 1,407
So, 9,849 is divisible by 7.
And 7 is a factor (divisor) of 9,849.
Also, the greatest factor (divisor) of 7 is the number itself, 7.
The greatest (highest) common factor (divisor),
gcf, hcf, gcd (7; 9,849) = 7
9,849 is divisible by 7
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.
7 is a prime number and cannot be broken down into other prime factors.
9,849 = 3 × 72 × 67
9,849 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 (7; 9,849) = 7
9,849 contains all the prime factors of the number 7
9,849 is divisible by 7.
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.