The longest factor string for 210 is not simply the factors multiplied together in a straightforward manner, such as (2 \times 3 \times 5 \times 7). Instead, it can involve breaking down these factors into smaller integers that multiply to 210, like (1 \times 2 \times 3 \times 5 \times 7) or any combination of these factors that maintain the product of 210. Therefore, a string that doesn't maximize the count of factors, such as (1 \times 210), is not the longest factor string.
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.
A factor string is a multiplication sentence. The smallest are the factor pairs, the largest 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.
200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210...yep all 11
210 is not prime.
Because if all the factors are prime, the factorization can't be broken down further. Consider some factor strings for 210: 2 x 105 2 x 3 x 35 2 x 3 x 5 x 7 The last (and longest) is the prime factorization.
The greatest common factor of 66 and 210 is 6.
Since 105 is a factor of 210, it is automatically the GCF.
The greatest common factor of 1200 and 210 is 30.
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.
It can be. 105 is a factor of 210.
The highest common factor of the numbers 210 and 330 is 30.
The greatest common factor of 154 , 210 = 14