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The number 24 can be made by multiplying together four prime numbers: 2, 2, 2 and 3. How many primes must be multiplied to make 2400?

 Apr 1, 2020
 #1
avatar+633 
+1

Prime Factoring:

2400

 

2 * 1200

 

2 * 2 * 600

 

2 * 2 * 2 * 300

 

2 * 2 * 2 * 2 * 150

 

2 * 2 * 2 * 2 * 2 * 75

 

2 * 2 * 2 * 2 * 2 * 5 * 15

 

2 * 2 * 2 * 2 * 2 * 5 * 5 * 3

 Apr 1, 2020
 #2
avatar+210 
0

Notice that 2400 is just 24*100. So, it will have the prime factors of 24 times plus those of 100, which are 2^2+5^2. Added together, that makes 8 primes.

 Apr 1, 2020

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