Write 583 as a product of its Prime Factors
To find the prime factorization of 583, we start by dividing it by the smallest prime number, which is 2. However, 583 is an odd number, so it is not divisible by 2.
Next, we try dividing it by the next prime number, which is 3. When we divide 583 by 3, we get a quotient of 194 with a remainder of 1.
Now, we move on to the next prime number, which is 5. However, 583 is not divisible by 5, as the last digit is not 0 or 5.
Next, we try dividing 583 by the next prime number, which is 7. When we divide it, we get a quotient of 83 with a remainder of 2.
Now, we move on to the next prime number, which is 11. When we divide 583 by 11, we get a quotient of 53 with a remainder of 0.
As the remainder is 0, we stop dividing. The primes we used to divide 583 were 3, 7, and 11.
Therefore, the prime factorization of 583 is 3 * 7 * 11.
But you said that 3 and 5 did NOT work!!!!
Apologies for the confusion. Let's find the prime factorization of 583 correctly.
We start by dividing 583 by the smallest prime number, 2. Since 583 is odd, it is not divisible by 2.
Next, we try dividing it by the next prime number, 3. When we divide 583 by 3, we get a quotient of 194 with a remainder of 1.
Now, we move on to the next prime number, which is 5. When we divide 583 by 5, we get a quotient of 116 with a remainder of 3.
Since 583 is not divisible by 5, we continue to the next prime number, which is 7. When we divide 583 by 7, we get a quotient of 83 with a remainder of 4.
Similarly, we move on to the next prime number, which is 11. When we divide 583 by 11, we get a quotient of 53 with no remainder.
As the quotient is a prime number, we stop dividing. The primes we used to divide 583 were 3, 5, 7, and 11.
Therefore, the prime factorization of 583 is 3 × 5 × 7 × 11.
11 worked, 3, 5 and 7 did not
Apologies for the mistakes. Let's find the correct prime factorization of 583.
We start by dividing 583 by the smallest prime number, 2. However, 583 is an odd number, so it is not divisible by 2.
Next, we try dividing it by the next prime number, 3. When we divide 583 by 3, we get a quotient of 194 with a remainder of 1.
Since 583 is not divisible by 3, we continue to the next prime number, which is 5. When we divide 583 by 5, we get a quotient of 116 with a remainder of 3.
Similarly, we move on to the next prime number, which is 7. When we divide 583 by 7, we get a quotient of 83 with a remainder of 4.
Lastly, we try dividing 583 by the next prime number, which is 11. When we divide 583 by 11, we get a quotient of 53 with no remainder.
As the quotient is a prime number, we stop dividing. The prime factors of 583 are 11 and 53.
Therefore, the prime factorization of 583 is 11 × 53.