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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.
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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 is the longest factor string for 42?
The longest factor string for 42 is when we break down 42 into its prime factors. 42 can be expressed as 2 x 3 x 7. This is the longest factor string because these are the prime numbers that, when multiplied together, result in 42.
What is the longest string of prime factors for 30?
the longest string of prime factor for 30 is 2 x 3 x 5
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 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.
