All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
Assuming you want all factors of a number: 1) Split a number into prime factors. 2) Combine the prime factors in all possible ways. To get the prime factors, you can systematically try out dividing the number by prime numbers, up to the number's square root (once the square of the prime number you try out is greater than the original number, you need not continue). For example, to find out prime factors of numbers up to 120, you only need to try dividing by 2, 3, 5, 7.
Factor trees are ways of notating the process of finding the prime factorization of a given composite number and, as such, should result in an identifiable string of prime factors.
(6375,1)(2125,3)(1275,5)(425,15)(375,17)(255,25)(125,51)(85,75)
I suspect that something very important is missing from your question. It would go between the words "write" and "as", and it would be a number. The answer to the question would be a positive whole number greater than ' 1 '.
Two ways: 5/5 = 1 and 5/1 = 5 because 5 is a prime number which has only 2 factors which are itself and one
Divide it by each prime number which does not have remainder.
Assuming you want all factors of a number: 1) Split a number into prime factors. 2) Combine the prime factors in all possible ways. To get the prime factors, you can systematically try out dividing the number by prime numbers, up to the number's square root (once the square of the prime number you try out is greater than the original number, you need not continue). For example, to find out prime factors of numbers up to 120, you only need to try dividing by 2, 3, 5, 7.
two possible ways 1 and the other number or the number an 1
One subset is prime numbers, since their factors are only 1 and the number itself. Other than that, there are many ways to end up with an even number of factors. The general equation for the number of factors is (p1+1)(p2+1) ... (p3 + 1) where the p values are the exponents of the prime factors of the number. So, as long as at least one prime factor is represented oddly (i.e., there is only 1, 3, 5... so on factors of that value in the prime factorization), then the number will have an even number of factors.
I'm not sure what you mean. But the factorization of a composite number into prime factors is unique, up to the ordering of the primes.
According to Wolfram Alpha, its prime factors are 11×79×2556067. (To get all of its factors, you can combine the prime factors in different ways.)
There are two ways in which the factors can be given. You are given all the prime factors (and their multiplicity). In that case simply multiply them all together. Or You are given each factor. In this case, the biggest of these is the number.
Factor trees are ways of notating the process of finding the prime factorization of a given composite number and, as such, should result in an identifiable string of prime factors.
There's a lot of different ways to notate the process (factor trees, rainbows, fireworks, division ladders, etc.) but the process itself is essentially the same. Divide a composite number by prime numbers until all the factors are prime.
(6375,1)(2125,3)(1275,5)(425,15)(375,17)(255,25)(125,51)(85,75)
First, you must find the factors of each number. The factors of 49 are {1, 7, 49} because [1 x 49] and [7 x 7] are the only ways to make 49 using multiplication. The factors of 8 are {1, 2, 4, 8} because [1 x 8] and [2 x 4] are the only ways to make 8 using multiplication. The Greatest Common Factor is {1} because 1 is the only number included in both the factors of 8 and the factors of 49. Alternate Method:The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.The prime factors of 8 are 2, 2, and 2.The prime factors of 49 are 7 and 7.There are no prime factors in common, so the numbers are relatively prime, which means the greatest common factor is 1.
I suspect that something very important is missing from your question. It would go between the words "write" and "as", and it would be a number. The answer to the question would be a positive whole number greater than ' 1 '.