Express 23150 as product of it prime factors .is it uniqe
You ask whether its prime factorization is unique.
The Fundamental Theorem of Arithmetic provess that it is.
To express 23150 as a product of its prime factors, we need to find all the prime numbers that divide the given number exactly.
We start by dividing 23150 by the smallest prime number, which is 2. After dividing, we get 23150 ÷ 2 = 11575.
Next, we divide the result, 11575, by another prime number, which is also 2. This gives us 11575 ÷ 2 = 5787.5. Since 5787.5 is not an integer, we cannot divide by 2 anymore.
The next prime number is 3. Dividing 5787 by 3 gives us 5787 ÷ 3 = 1929.
We continue dividing the resulting numbers by prime numbers until we obtain a result that is a prime number itself. Dividing 1929 by the next prime number, 3, gives us 1929 ÷ 3 = 643.
Since 643 is a prime number, we have found all the prime factors of 23150. The prime factors are 2, 2, 3, 3, and 643.
So, 23150 = 2 * 2 * 3 * 3 * 643.
Now, to answer your second question, whether the prime factorization is unique or not, we can observe that the order in which we write the prime factors does not matter. However, the prime factors themselves must remain the same.
In the case of 23150, the prime factorization is not unique because we can rearrange the prime factors to get a different representation, for example, 23150 = 2 * 3 * 2 * 3 * 643.
Therefore, the prime factorization of 23150 is not unique.
start off small.
23150 = 2315 * 2 * 5
2315 = 5 * 463
Now see whether you can find factors of 463...