Certainly! Let's find the prime factors of the number 50 step-by-step.
1. Definition of Prime Factors:
Prime factors of a number are the prime numbers that divide the original number exactly, without leaving a remainder.
2. Step-by-Step Solution:
Step 1: Start with the smallest prime number, which is 2.
- Divide [tex]\(50\)[/tex] by [tex]\(2\)[/tex]:
[tex]\[
50 \div 2 = 25
\][/tex]
Since [tex]\(50\)[/tex] is divisible by [tex]\(2\)[/tex], [tex]\(2\)[/tex] is a prime factor. The quotient is [tex]\(25\)[/tex].
Step 2: Now consider the number [tex]\(25\)[/tex]. The next smallest prime number is [tex]\(3\)[/tex], but [tex]\(25\)[/tex] is not divisible by [tex]\(3\)[/tex] (since [tex]\(25 \div 3\)[/tex] is not an integer). We then try the next prime number, which is [tex]\(5\)[/tex].
- Divide [tex]\(25\)[/tex] by [tex]\(5\)[/tex]:
[tex]\[
25 \div 5 = 5
\][/tex]
Since [tex]\(25\)[/tex] is divisible by [tex]\(5\)[/tex], [tex]\(5\)[/tex] is a prime factor, and the quotient is [tex]\(5\)[/tex].
Step 3: Now consider the number [tex]\(5\)[/tex]. Divide [tex]\(5\)[/tex] by [tex]\(5\)[/tex]:
[tex]\[
5 \div 5 = 1
\][/tex]
Since [tex]\(5\)[/tex] is divisible by [tex]\(5\)[/tex], [tex]\(5\)[/tex] is a prime factor, and the quotient is [tex]\(1\)[/tex].
Step 4: We stop here because our quotient is [tex]\(1\)[/tex], indicating that we have fully factored the original number.
3. Result:
Collecting all the prime factors we found:
[tex]\[
\boxed{2, 5, 5}
\][/tex]
So, the prime factors of [tex]\(50\)[/tex] are [tex]\(2\)[/tex], [tex]\(5\)[/tex], and [tex]\(5\)[/tex].
