21,985,599 and 0: Calculate all the common factors (divisors) of the two numbers (and the prime factors)

The common factors (divisors) of the numbers 21,985,599 and 0

The common factors (divisors) of the numbers 21,985,599 and 0 are all the factors of their 'greatest (highest) common factor (divisor)'.

To 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:
A = B × C. Example: 60 = 2 × 30.

Both B and C are factors of A and they both evenly divide A ( = without a remainder).

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

gcf, hcf, gcd (0; n1) = n1, where n1 is a natural number.

gcf, hcf, gcd (21,985,599; 0) = 21,985,599

Zero is divisible by any number other than zero (there is no remainder when dividing zero by these numbers)

>> The greatest (highest) common factor (divisor)

Preliminary step to take before finding all the factors:

To find all the factors (all the divisors) of the 'gcf', we need to break 'gcf' down into its prime factors (to build its prime factorization, to decompose it into prime factors, to write it as a product of prime numbers).

The prime factorization of the greatest (highest) common factor (divisor):

The prime factorization of a number (the decomposition of the number into prime factors, breaking down the number into prime numbers): finding the prime numbers that multiply together to make that number.

21,985,599 = 3 × 43 × 131 × 1,301
21,985,599 is not a prime number but a composite one.

* The natural numbers that are divisible only 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.

>> The prime factorization

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

Multiply the prime factors involved in the prime factorization of the GCF in all their unique combinations, that give different results.

gcf, hcf, gcd = 21,985,599 = 3 × 43 × 131 × 1,301

Also add 1 to the list of factors (divisors). All the numbers are divisible by 1.

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

The list of factors (divisors):

neither prime nor composite = 1

prime factor = 3

prime factor = 43

3 × 43 = 129

prime factor = 131

3 × 131 = 393

prime factor = 1,301

3 × 1,301 = 3,903

43 × 131 = 5,633

3 × 43 × 131 = 16,899

43 × 1,301 = 55,943

3 × 43 × 1,301 = 167,829

131 × 1,301 = 170,431

3 × 131 × 1,301 = 511,293

43 × 131 × 1,301 = 7,328,533

3 × 43 × 131 × 1,301 = 21,985,599

The final answer:
(scroll down)

21,985,599 and 0 have 16 common factors (divisors):
1; 3; 43; 129; 131; 393; 1,301; 3,903; 5,633; 16,899; 55,943; 167,829; 170,431; 511,293; 7,328,533 and 21,985,599
out of which 4 prime factors: 3; 43; 131 and 1,301

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.

Other similar operations to the common factors:

What are all the common factors (divisors and prime factors) of the numbers 21,985,591 and 1,000,000,000,000?

What are all the common factors (divisors and prime factors) of the numbers 21,985,609 and 11?

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

The common factors (divisors) of 21,985,599 and 0 = ?	May 29 02:06 UTC (GMT)
The common factors (divisors) of 69 and 1 = ?	May 29 02:06 UTC (GMT)
The common factors (divisors) of 6,668 and 149 = ?	May 29 02:06 UTC (GMT)
The common factors (divisors) of 21 and 0 = ?	May 29 02:06 UTC (GMT)
The common factors (divisors) of 118 and 0 = ?	May 29 02:06 UTC (GMT)
The list of all the calculated factors (divisors) of one or 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)

If the number "t" is a factor (divisor) of the number "a" then in the prime factorization of "t" we will only encounter prime factors that also occur in the prime factorization of "a".
If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" (powers, or multiplicities) is at most equal to the exponent of the same base that is involved in the prime factorization of "a".
Hint: 2³ = 2 × 2 × 2 = 8. 2 is called the base and 3 is the exponent. 2³ is the power and 8 is the value of the power. We sometimes say that the number 2 is raised to the power of 3.

For example, 12 is a factor (divisor) of 120 - the remainder is zero when dividing 120 by 12.
Let's look at the prime factorization of both numbers and notice the bases and the exponents that occur in the prime factorization of both numbers:
12 = 2 × 2 × 3 = 2² × 3
120 = 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5
120 contains all the prime factors of 12, and all its bases' exponents are higher than those of 12.

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 the prime factorizations of both "a" and "b".
If there are exponents involved, the maximum value of an exponent for any base of a power that is found in the prime factorization of "t" is at most equal to the minimum of the exponents of the same base that is involved in the prime factorization of both "a" and "b".

For example, 12 is the common factor of 48 and 360.
The remainder is zero when dividing either 48 or 360 by 12.
Here there are the prime factorizations of the three numbers, 12, 48 and 360:
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, of two numbers, "a" and "b", is the product of all the common prime factors involved in the prime factorizations of both "a" and "b", taken by the lowest exponents.
Based on this rule it is calculated the greatest common factor, GCF, (or the greatest common divisor GCD, HCF) of several numbers, as shown in the example below...

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

Coprime numbers:
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).

Factors of the GCF
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".