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Do larger numbers have more factors than smaller numbers?
Generally yes, but not in all cases. The largest prime number has over 22 million digits but only two factors whereas 60 has six times as many factors.
Explain Why the Numbers 0 and 1 have no prime factor?
2 is the smallest prime number. Numbers can't have factors larger than themselves. Zero and one aren't large enough to have prime factors.
Composite numbers vs prime numbers?
A composite number is a natural number that can be divided into smaller factors (which are also natural numbers). For example, 6 = 2 x 3. A prime number is an integer (greater than 1) that cannot be separated into smaller factors. For example, 7 can't be divided into smaller factors.
Are there prime numbers that are also square mumbers?
No. That isn't possible: A prime number, by definition, has no smaller factors. A square number does have a smaller factor - the number that is squared.
What are two numbers whose greatest common factor is 7 and whose sum is 105 such that the larger is twice the smaller and the smaller has only two prime factors?
Since one number is twice the other, the smaller number must be the greatest common factor. Since the greatest common factor is 7, that would make the other number 14. But, 7 is a prime number and has only one prime factor. However, the larger number, 14, has two prime factors. Also, the sum of the two numbers is 21, not 105. So, the information in the problem does not have a solution. Let us ignore the greatest common factor information. Let the smaller number be x. That means the larger number is 2x. x + 2x = 105 => 3x = 105 => x = 35. The two numbers are 35 and 70. The greatest common factor is 35. The smaller number, 35, has only two prime factors.
