How to count the number of factors of a number?
Without actually finding the factors
- 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 = (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 × 2 = 24
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):
Numbers other than 1 that are not prime factors are composite instead.
neither prime nor composite =
1
prime factor =
3
prime factor =
5
composite factor = 3
2 =
9
composite factor = 3 × 5 =
15
composite factor = 3
2 × 5 =
45
prime factor =
79
composite factor = 3 × 79 =
237
composite factor = 5 × 79 =
395
composite factor = 3
2 × 79 =
711
composite factor = 3 × 5 × 79 =
1,185
composite factor = 3
2 × 5 × 79 =
3,555
This list continues below...
... This list continues from above
prime factor =
840,451
composite factor = 3 × 840,451 =
2,521,353
composite factor = 5 × 840,451 =
4,202,255
composite factor = 3
2 × 840,451 =
7,564,059
composite factor = 3 × 5 × 840,451 =
12,606,765
composite factor = 3
2 × 5 × 840,451 =
37,820,295
composite factor = 79 × 840,451 =
66,395,629
composite factor = 3 × 79 × 840,451 =
199,186,887
composite factor = 5 × 79 × 840,451 =
331,978,145
composite factor = 3
2 × 79 × 840,451 =
597,560,661
composite factor = 3 × 5 × 79 × 840,451 =
995,934,435
composite factor = 3
2 × 5 × 79 × 840,451 =
2,987,803,305
24 common factors (divisors)
What times what is 2,987,803,305?
What number multiplied by what number equals 2,987,803,305?
All the combinations of any two natural numbers whose product equals 2,987,803,305.
1 × 2,987,803,305 = 2,987,803,305
3 × 995,934,435 = 2,987,803,305
5 × 597,560,661 = 2,987,803,305
9 × 331,978,145 = 2,987,803,305
15 × 199,186,887 = 2,987,803,305
45 × 66,395,629 = 2,987,803,305
79 × 37,820,295 = 2,987,803,305
237 × 12,606,765 = 2,987,803,305
395 × 7,564,059 = 2,987,803,305
711 × 4,202,255 = 2,987,803,305
1,185 × 2,521,353 = 2,987,803,305
3,555 × 840,451 = 2,987,803,305
12 unique multiplications