Write 50 as a product of prime factors
The correct answer and explanation is:
The number 50 can be written as a product of prime factors by breaking it down into its prime components.
First, start by dividing 50 by the smallest prime number, which is 2. Since 50 is even, it is divisible by 2:
50 ÷ 2 = 25
Now, 2 is a prime factor. Next, factorize 25. The smallest prime number that divides 25 is 5:
25 ÷ 5 = 5
Since 5 is also a prime number, factorization stops here.
Putting it all together, the prime factors of 50 are:
2 × 5 × 5
This can also be written as:
2 × 5²
So, the prime factorization of 50 is 2 multiplied by 5 squared.
Explanation:
Prime factorization is the process of expressing a number as a product of prime numbers. Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. Every composite number can be uniquely factored into primes, according to the Fundamental Theorem of Arithmetic.
Starting with the smallest prime helps simplify the factorization process. For 50, since it is even, dividing by 2 first breaks it down efficiently. Once 2 is factored out, the remaining number is 25, which is not divisible by 2 but divisible by 5. Since 5 is prime, the factorization is complete.
Prime factorization is useful in many areas of mathematics such as finding the greatest common divisor (GCD), least common multiple (LCM), simplifying fractions, and solving problems related to divisibility. Representing numbers as products of primes reveals their building blocks and helps in understanding their properties.
Therefore, expressing 50 as a product of prime factors yields 2 × 5².