what is the positive difference between the two largest prime factors of 159,137?
To find the positive difference between the two largest prime factors of 159,137, we need to determine the prime factors of this number.
First, let's find the prime factors by dividing 159,137 by prime numbers starting from 2. We cannot divide evenly by 2, so we continue to the next prime number, which is 3.
159,137 ÷ 3 = 53,045.67
Since the result is not a whole number, we move on to the next prime number, which is 5.
159,137 ÷ 5 = 31,827.4
Again, the result is not a whole number. We continue this process with larger prime numbers until we find the prime factors.
159,137 is not divisible by 7.
159,137 ÷ 11 = 14,467.91
Still, the result is not a whole number.
159,137 ÷ 13 = 12,245.92
The result is not a whole number.
159,137 ÷ 17 = 9,361
Finally, we have found a whole number result. Thus, the prime factors of 159,137 are 17 and 9,361.
To find the positive difference between the two largest prime factors, we subtract the smaller prime factor from the larger one.
The larger prime factor is 9,361, and the smaller prime factor is 17.
9,361 - 17 = 9,344
Therefore, the positive difference between the two largest prime factors of 159,137 is 9,344.
To find the positive difference between the two largest prime factors of 159,137, we first need to determine what the prime factors of 159,137 are.
One approach is to start by finding the smallest prime number that divides evenly into 159,137, which is 7. Dividing 159,137 by 7 yields a quotient of 22,733 with a remainder of 6. Since 6 is not divisible by any prime numbers, we move on to the next prime number, which is 11. Dividing 22,733 by 11 results in a quotient of 2,057 with a remainder of 6. Again, 6 is not divisible by any prime numbers, so we continue.
Now we divide 2,057 by the next prime number, which is 13. Dividing yields a quotient of 158 with a remainder of 11. In this case, 11 is a prime number, so we have found one of the prime factors of 159,137. Continuing, we divide 158 by another prime number, which is 2. Dividing gives us a quotient of 79 with no remainder. 79 is also a prime number, so we have found another prime factor of 159,137.
To summarize, the prime factorization of 159,137 is 7 * 11 * 13 * 2 * 79.
From this, we can see that the two largest prime factors are 79 and 13. To find the positive difference between these two numbers, we subtract the smaller prime factor from the larger prime factor: 79 - 13 = 66.
Therefore, the positive difference between the two largest prime factors of 159,137 is 66.