gcf (214; 3,210) = ? Calculate the greatest (highest) common factor (divisor) of numbers, gcf (hcf, gcd), by two methods: 1) The numbers' divisibility and 2) The prime factorization

gcf, hcf, gcd (214; 3,210) = ?

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:


3,210 ÷ 214 = 15 + 0


=> 3,210 = 214 × 15


So, 3,210 is divisible by 214.


And 214 is a factor (divisor) of 3,210.


The greatest (highest) common factor (divisor):
gcf, hcf, gcd (214; 3,210) = 214


gcf, hcf, gcd (214; 3,210) = 214 = 2 × 107
3,210 is divisible by 214

Method 2. The prime factorization:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.


214 = 2 × 107
214 is not a prime number but a composite one.


3,210 = 2 × 3 × 5 × 107
3,210 is not a prime number but a composite one.


* The natural numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has exactly 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):

Multiply all the common prime factors, taken by their smallest powers (exponents).


gcf, hcf, gcd (214; 3,210) = 2 × 107



gcf, hcf, gcd (214; 3,210) = 2 × 107 = 214
3,210 contains all the prime factors of the number 214.

The final answer:
The greatest (highest) common factor (divisor),
gcf, hcf, gcd (214; 3,210) = 214 = 2 × 107
3,210 is divisible by 214.
3,210 contains all the prime factors of the number 214.

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 operations of the same kind:


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.

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The Euclidean Algorithm

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