What is the prime factorization of 20
The Correct Answer and Explanation is:
To find the prime factorization of 20, we begin by dividing it by the smallest prime number, 2, since 20 is an even number.
- Divide by 2:
20÷2=1020 ÷ 2 = 1020÷2=10
So, 2 is a factor of 20, and we are left with 10. - Divide 10 by 2 again:
10÷2=510 ÷ 2 = 510÷2=5
Now, we have another factor of 2, and we are left with 5. - Prime check for 5:
5 is a prime number because it can only be divided by 1 and itself. We stop here since no further division is possible.
Therefore, the prime factorization of 20 is:
20=2×2×520 = 2 \times 2 \times 520=2×2×5
In exponential form, we can express it as:
20=22×520 = 2^2 \times 520=22×5
Explanation:
Prime factorization involves breaking down a number into the product of prime numbers. Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. In the case of 20, it is first divided by 2, the smallest prime, because 20 is even. After dividing by 2 twice, we are left with 5, which is a prime number. Hence, the prime factorization of 20 is 22×52^2 \times 522×5. This tells us that 20 is made up of two 2s and one 5.
Understanding prime factorization is important for simplifying expressions, finding greatest common divisors, and solving problems in number theory.
