126 and 175: Calculate all the common factors (divisors) of the two numbers (and the prime factors)

The common factors (divisors) of the numbers 126 and 175

The common factors (divisors) of the numbers 126 and 175 are all the factors of their 'greatest (highest) common factor (divisor)'.

Remember

A factor (divisor) of a natural number A is a natural number B which when multiplied by another natural number C equals the given number A. Both B and C are factors of A and they both evenly divide A ( = without a remainder).



Calculate the greatest (highest) common factor (divisor). Follow the two steps below.

The prime factorization of numbers:

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


126 = 2 × 32 × 7
126 is not a prime number but a composite one.


175 = 52 × 7
175 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), gcf, hcf, gcd:

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


gcf, hcf, gcd (126; 175) = 7




Find all the factors (divisors) of the greatest (highest) common factor (divisor), gcf, hcf, gcd

7 is a prime number and cannot be broken down into other prime factors.


A prime number has exactly two factors: 1 and itself.


All the factors (divisors) are listed below - in ascending order.



The list of factors (divisors):

neither prime nor composite = 1
prime factor = 7

The final answer:
(scroll down)

126 and 175 have 2 common factors (divisors):
1 and 7
out of which 1 prime factor: 7

A quick way to find the factors (the divisors) of a number is to first have its prime factorization.


Then multiply the prime factors in all the possible combinations that lead to different results and also take into account their exponents, if any.


The latest 5 sets of calculated factors (divisors): of one number or the common factors of two numbers

Calculate all the divisors (factors) of the given numbers

How to calculate (find) all the factors (divisors) of a number:

Break down the number into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

To calculate the common factors of two numbers:

The common factors (divisors) of two numbers are all the factors of the greatest common factor, gcf.

Calculate the greatest (highest) common factor (divisor) of the two numbers, gcf (hcf, gcd).

Break down the GCF into prime factors. Then multiply its prime factors in all their unique combinations, that give different results.

Factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)


What is a prime number? Definition, examples

What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

Completely reduce (simplify) fractions to the lowest terms: Steps and Examples