The common factors (divisors) of the numbers 18,500,274 and 0?
The common factors of the numbers 18,500,274 and 0 are all the factors of their 'greatest common factor', gcf
Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:
Zero is divisible by any number other than zero (there is no remainder when dividing zero by these numbers).
The greatest factor (divisor) of the number 18,500,274 is the number itself.
⇒ gcf, hcf, gcd (18,500,274; 0) = 18,500,274
To find all the factors (all the divisors) of the 'gcf', we need its prime factorization (to decompose it into prime factors).
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
18,500,274 = 2 × 32 × 13 × 173 × 457
18,500,274 is not a prime number but a composite one.
- Prime number: a natural number that is divisible only 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.
How to count the number of factors of a number?
- If a number N is prime factorized as:
N = am × bk × cz
where a, b, c are the prime factors and m, k, z are their exponents, natural numbers, .... - ...
- Then the number of factors of the number N can be calculated as:
n = (m + 1) × (k + 1) × (z + 1) - ...
- In our case, the number of factors is calculated as:
- n = (1 + 1) × (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 3 × 2 × 2 × 2 = 48
But to actually calculate the factors, see below...
3. Multiply the prime factors of the 'gcf':
Multiply the prime factors involved in the prime factorization of the GCF in all their unique combinations, that give different results.
Also consider the exponents of the prime factors (example: 32 = 3 × 3 = 9).
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 =
2
prime factor =
3
2 × 3 =
6
3
2 =
9
prime factor =
13
2 × 3
2 =
18
2 × 13 =
26
3 × 13 =
39
2 × 3 × 13 =
78
3
2 × 13 =
117
prime factor =
173
2 × 3
2 × 13 =
234
2 × 173 =
346
prime factor =
457
3 × 173 =
519
2 × 457 =
914
2 × 3 × 173 =
1,038
3 × 457 =
1,371
3
2 × 173 =
1,557
13 × 173 =
2,249
2 × 3 × 457 =
2,742
2 × 3
2 × 173 =
3,114
3
2 × 457 =
4,113
This list continues below...