2,756 and 175: All the common factors (divisors) and prime factors of the integer numbers

The common factors (divisors) of 2,756 and 175 are all the factors (divisors) of their 'greatest (highest) common factor (divisor)'

Note

Factor of a number A: a number B that when multiplied with another C produces the given number A. Both B and C are factors of A.



Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd. Follow the two steps below.

Integer numbers prime factorization:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


2,756 = 22 × 13 × 53;
2,756 is not a prime, is a composite number;


175 = 52 × 7;
175 is not a prime, is a composite number;


* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.




Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd

Multiply all the common prime factors, by the lowest exponents (if any).
But the two numbers have no common prime factors.


Greatest (highest) common factor (divisor):


gcf, hcf, gcd (2,756; 175) = 1;
coprime numbers (relatively prime);




Find all the factors (divisors) of the GCF (HCF, GCD), 1

1 is divisible only by itself.


1 cannot be factored, cannot be broken down to prime factors.


1 is considered neither a prime nor a composite number.


Any number is divisible by 1.



neither a prime nor a composite = 1


Final answer:

2,756 and 175 have 1 common factor (divisor): 1
coprime numbers (relatively prime)
1 is considered neither a prime nor a composite number.

More operations of this kind:

Calculator: all the (common) factors (divisors) of numbers

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

If "t" is a factor (divisor) of "a" then among the prime factors of "t" will appear only prime factors that also appear on the prime factorization of "a" and the maximum of their exponents (powers, or multiplicities) is at most equal to those involved in the prime factorization of "a".

For example, 12 is a factor (divisor) of 60:

  • 12 = 2 × 2 × 3 = 22 × 3
  • 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5

If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in both the prime factorizations of "a" and "b", by lower or at most by equal powers (exponents, or multiplicities).

For example, 12 is the common factor of 48 and 360. After running both numbers' prime factorizations (factoring them down to prime factors):

  • 12 = 22 × 3;
  • 48 = 24 × 3;
  • 360 = 23 × 32 × 5;
  • Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.

The greatest common factor, GCF, is the product of all prime factors involved in both the prime factorizations of "a" and "b", by the lowest powers (multiplicities).

Based on this rule it is calculated the greatest common factor, GCF, (or greatest common divisor GCD, HCF) of several numbers, as shown in the example below:

  • 1,260 = 22 × 32;
  • 3,024 = 24 × 32 × 7;
  • 5,544 = 23 × 32 × 7 × 11;
  • Common prime factors are: 2 - its lowest power (multiplicity) is min.(2; 3; 4) = 2; 3 - its lowest power (multiplicity) is min.(2; 2; 2) = 2;
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252;

If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).

If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".


What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples