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A factor string consists of any factors (except 1) that multiply to equal the number. Prime factorization consists of only prime numbers that multiply to equal the number. In the case where the factors of the original number consists only of primes, there is no difference.
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What is a prime factor string?
A prime factor string is a way to express a number by listing its prime factors along with their respective exponents. For example, for the number 60, the prime factorization is (2^2 \times 3^1 \times 5^1). The "prime factor string" in this case is a formatted representation that captures this factorization. It shows each prime factor and the number of times it divides the original number.
What is the prime factorization the longest factor string for 40?
2 x 2 x 2 x 5 = 40
How do you find the factor string for a number?
Factor strings are multiplication sentences. You can take any factor pair, put a multiplication symbol between them and you have a factor string. The longest factor string for any composite number is the prime factorization. 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. And the longest factor string.
What are factors and string and length?
Factors are integers that can be multiplied together to create a product. Such multiplication sentences are called strings. The length of the string is how many numbers are in it. 6 x 4 is a factor string for 24. 2 x 3 x 4 is a longer factor string for 24. 2 x 2 x 2 x 3 is the longest factor string for 24. The longest factor string is also known as the prime factorization.
The longest string of factors for a number?
The prime factorization.
What is a longest factor string?
The prime factorization is the longest factor sting.
What is the longest factor string you found?
The longest factor string of any composite number is its prime factorization.
How do you know you have the biggest factor string?
When all of the factors are prime. The longest factor string is the prime factorization.
Is the prime factorization the same as the factor string?
Factor strings don't necessarily have to be composed entirely of prime numbers. But the longest factor string, the one that is entirely prime numbers, that's the prime factorization.
Is factor string the same as factor tree?
Not really. A factor string is a multiplication sentence. A factor tree is a way of notating the process of finding the prime factorization of a given number. End result: 4 x 9 can be a factor string for 36, but can't be a prime factorization. The prime factorization of 36 is 2 x 2 x 3 x 3.
What is the longest factor string of a number called?
The prime factorization
What is the factor string of 85 in prime factorization?
The prime factorization of 85 is: 5 x 17
Is prime factorization and longest factor string the same thing?
Yes.
Is 10 and 24 a factorization of 240?
10 x 24 = 240, but it's considered a factor string, not a full factorization.
What number has the prime factorization of 4x5x49?
That's a factor string of 980; it is not the prime factorization. 4 and 49 aren't prime.
What are the longest factor string for 840 and explain why?
The longest factor string for 840 is its prime factorization because prime factors can't be broken down any further.
What is the factor of 81x2x2x2x2?
81 x 24 is a factor string for 1296. The full prime factorization of 1296 is 24 x 34
