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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.
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What is a factor string?
A factor string is a name for a number written as a product of two or more factors. In a factor string, 1 may not be used as a factor. For example, a factor string for 24 is 2 X 3 X 4, or 2 3 4.:0
What is the definition for Factor Strings?
A factor string is a name for a number sentence written as a product of two or more factors.2 x 3 is a factor string for 6.
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 difference between a factor string and prime factorization?
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.
What is the longest factor string of 30?
The longest factor string of 30 is 2 x 3 x 5.
