WHAT IS THE PRIME FACTORIZATION OF 45? and what is the sum of the only two prime numbers that differ by one ? Thank you
45 = 3^2 5^1
2+3 = 5
Thank you , but could you explain the factorization of 45? Idont get it
The easiest way to find the factors is to start with the smallest prime, and see whether it is a factor. Continue dividing successive primes until all you are left with is 1.
Is 2 a factor of 45? No.
How about he next prime (3)?
3 divides 45 twice, so 3^2 is included in the list.
45/3^2 = 5, so we keep going.
5 divides 5 once, so 5^1 is in the list.
5/5 = 1, so we are done.
The list of factors is 3^2 5^1
Consider 166600
166600/2 = 83300
83300/2 = 41650
41650/2 = 20825
2 does not divide 20825, so 2^3 is in the list
3 does not divide 20825
20825/5 = 4165
4165/5 = 833
5 does not divide 833, so 5^2 is in the list
833/7 = 119
119/7 = 17
7 does not divide 17, so 7^2 is in the list
17 is prime, so the final factorization is
2^3 5^2 7^2 17
As you can see, the method is quite simple, but very cumbersome for large numbers.
Igot it now. Thank you so much
To find the prime factorization of 45, we need to determine the prime numbers that multiply together to equal 45. Here's how we can do it step by step:
1. Start by dividing 45 by the smallest prime number, which is 2. Since 45 is not divisible by 2, move on to the next prime number, which is 3.
2. Divide 45 by 3. The result is 15, with no remainder.
3. Now we divide 15 by the smallest prime number, which is 2. But as mentioned earlier, 45 is not divisible by 2, so we proceed to the next prime number, which is 3.
4. Divide 15 by 3. The result is 5, with no remainder.
5. We are left with 5, which is a prime number itself.
Therefore, the prime factorization of 45 is 3 * 3 * 5, which can also be written as 3^2 * 5.
Now, let's move on to the next part of your question about two prime numbers that differ by one.
To find the sum of the only two prime numbers that differ by one, we need to identify these two prime numbers and then add them together. The prime numbers that differ by one are known as twin primes.
One pair of twin primes is 5 and 7. Both 5 and 7 are prime numbers, and they differ by one.
Therefore, the sum of the only two prime numbers that differ by one is 5 + 7 = 12.
So, the prime factorization of 45 is 3^2 * 5, and the sum of the only two prime numbers that differ by one is 12.