Ex. 23 and 24
23 is prime.
24 is composite.
2 x 2 x 2 x 3 = 24
2^3 x 3 = 24
Yes. Any composite number can be expressed as a product of prime factors.
A number can be factored to determine whether it is prime or composite. A prime number has exactly 2 factors, 1 and the number itself. A composite number has more than two factors.
As a product of its prime factors in exponents: 22*3*52 = 300
Exponents are used to replace repeated factors. Prime numbers won't use exponents because they don't have repeated factors. To express the prime factorization of a particular composite number using exponents, just count. 2 x 2 x 2 x 3 x 3 = 72 23 x 32 = 72
When the expression is broken down into its prime factors it is factored completely.
Yes.
Yes. Any composite number can be expressed as a product of prime factors.
24 is composite because it can factored or split up as 24 = 3 * 8 for example. Prime numbers, such as 23, can not be split into factors.
A number can be factored to determine whether it is prime or composite. A prime number has exactly 2 factors, 1 and the number itself. A composite number has more than two factors.
Yes. Consider the trinomial x2 + 2x + 4. It can be factored as (x+2)(x+2), that is to say, it has two identical factors of (x+2).
The exponent just counts the number of times the factor is repeated. 2 x 2 x 2 x 3 x 3 = 72 23 x 32 = 72
As a product of its prime factors in exponents: 22*3*52 = 300
Composite numbers are those numbers greater than 1, that have more than 2 factors. Your question is too ambiguous! I don't completely agree with the words above. Composite numbers are all numbers that are not prime numbers. In other words, composite numbers are divisible by other numbers besides themselves and 1. To find the number of factors in a composite number, put the number into prime factored form. For example, the number 24 in prime factored form is 2^3 X 3^1. To find the number of factors of 24, add the number 1 to each of the exponents and multiply their sums. The exponent of 2 is 3, and the exponent of 3 is 1, so (3+1)(1+1) = 4 X 2 = 8. There are eight factors of 24. They are: 1,2,3,4,6,8,12,24. Here's my question: does anyone know the name or concept behind this algorithm, including more like them? Thanks.
If you know a number is composite, then you also know that it can be factored into more factors than just 1 and itself. A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite.
Yes. The Fundamental Theorem of Arithmetic states that every composite number has one and only one prime factorization; the above is one expression of this fact.
Exponents are used to replace repeated factors. Prime numbers won't use exponents because they don't have repeated factors. To express the prime factorization of a particular composite number using exponents, just count. 2 x 2 x 2 x 3 x 3 = 72 23 x 32 = 72
Oh, dude, of course! A composite number is just a number that can be broken down into smaller numbers, like a Lego set. And prime factors are the prime numbers that multiply together to give you that composite number. So, like, yeah, you can totally factor a composite number into prime factors. It's like breaking down a complicated recipe into its basic ingredients.