Write the number 45 as a product of prime factor 45
The correct answer and explanation is:
Answer:
The number 45 can be written as a product of prime factors as:
45 = 3 × 3 × 5 or 45 = 3² × 5
Explanation:
Prime factorization is the process of expressing a composite number as a product of its prime numbers. Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. Examples include 2, 3, 5, 7, 11, and so on.
To find the prime factors of 45, follow these steps:
- Start dividing by the smallest prime number, 2:
Since 45 is odd, it’s not divisible by 2. - Try the next prime number, 3:
45 ÷ 3 = 15
So, 3 is a prime factor. - Continue factoring 15:
15 ÷ 3 = 5
Here, 3 is again a factor, and 5 is the quotient. - Check if 5 is prime:
Yes, 5 is a prime number.
At this point, we have completely factored 45 into prime numbers: 3, 3, and 5.
Therefore:
45 = 3 × 3 × 5 = 3² × 5
Why is prime factorization important?
- Fundamental Theorem of Arithmetic: Every positive integer greater than 1 can be expressed uniquely as a product of prime numbers, except for the order of the factors. This theorem guarantees that the prime factorization is unique.
- Simplifying fractions: Prime factors help in reducing fractions to their simplest form by canceling common factors.
- Finding the Greatest Common Divisor (GCD) and Least Common Multiple (LCM): These are calculated easily using prime factorizations of the numbers involved.
- Cryptography and Computer Science: Prime factorization plays a vital role in security algorithms, such as RSA encryption.
By understanding the prime factors of a number like 45, we gain insight into its divisibility properties and can solve many mathematical problems more efficiently.