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Why is the longest factor string for any whole number is the prime factorization?
Shorter factor strings aren't composed entirely of prime numbers.
How many distinct strings of factors are there for a given number?
It varies with each given number.
What is a number that is the product of a distinct factor multiplied by itself?
It is a square of that factor. E.g. 5 is a distinct factor of 25. If you multiply that distinct factor by itself (5*5) you get 25. A square comes from the x^2 notation and is any number which has a factor which is multiplied by itself.
What is the difference between factor pairs and distinct factor pairs?
The difference is between factor pairs and distinct factors. With square numbers, one of the factor pairs will be the same number twice. When listing the distinct factors, that number is only listed once.
What are the factor strings for the number 25?
5 x 5
What is the longest factor string you found?
The longest factor string of any composite number is its prime factorization.
What is the longest factor string for 312?
The longest factor string is 2x2x2x3x13. It is always best to list your factor string from the least to greatest number.
How many longest strings of factors are there for a given number?
For composite numbers, only one string of factors is the longest; the prime factorization.
What is a number that is a product of a distinct factor multiplied by itself?
A perfect square
Is 12 the smallest distinct prime factor?
No, 12 is not a prime number.
How many distinct positive integer factor does the number 80 have?
10 of them.
What is the longest factor string of a number called?
The prime factorization
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