the number 34,459,425 is the product of several consecutive positive odd numbers. what is the greatest of these numbers?
I do not know how to solve this, but I think it has something to do with factorials (x!)
To find the greatest consecutive positive odd number that multiplies to give the number 34,459,425, we can use prime factorization. Here's how you can do it:
1. Begin by finding the prime factorization of 34,459,425. Divide the number by the smallest prime number, which is 2. Keep dividing until you can't divide any further. This will give you the prime factors.
34,459,425 ÷ 2 = 17,229,712.5 (cannot be divided by 2 evenly)
34,459,425 is an odd number, so it cannot be divided by 2.
34,459,425 ÷ 3 = 11,486,475 (cannot be divided by 3 evenly)
34,459,425 ÷ 5 = 6,891,885
6,891,885 ÷ 5 = 1,378,377
1,378,377 ÷ 7 = 197,625.2857 (cannot be divided by 7 evenly)
197,625 ÷ 5 = 39,525
39,525 ÷ 3 = 13,175
13,175 ÷ 5 = 2,635
2,635 ÷ 5 = 527
527 ÷ 17 = 31
31 is a prime number, so we stop the process here.
2. Now, we need to find the largest consecutive odd number that multiplies to give 34,459,425. This can be achieved by taking the product of all the prime factors we found: 5 × 5 × 3 × 3 × 17 × 31 = 34,459,425.
Therefore, the greatest consecutive odd number in the product is 31.