1. Carry out the prime factorization of the number 7,007:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
7,007 = 72 × 11 × 13
7,007 is not a prime number but a composite one.
* Prime number: a natural number that is divisible (divided evenly) only by 1 and itself. A prime number has exactly two factors: 1 and the number 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 = (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12
But to actually calculate the factors, see below...
2. Multiply the prime factors of the number 7,007
Multiply the prime factors involved in the prime factorization of the number in all their unique combinations, that give different results.
Also consider the exponents of these prime factors.
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 =
7
prime factor =
11
prime factor =
13
7
2 =
49
7 × 11 =
77
This list continues below...
7,007 has 12 factors (divisors):
1; 7; 11; 13; 49; 77; 91; 143; 539; 637; 1,001 and 7,007
out of which 3 prime factors: 7; 11 and 13
7,007 and 1 are sometimes called improper factors, the others are called proper factors (proper divisors).
A quick way to find the factors (the divisors) of a number is to break it down into prime factors.
Then multiply the prime factors and their exponents, if any, in all their different combinations.