Number N = 26 * 55 * 76 * 107; how many factors of N are even numbers?
1183
1200
1050
840
Answers
How many even factors does a number have? Now that's a rather odd question. Think about that.
The prime factorization of 26 * 55 * 76 * 107 is 213 * 512 * 76.
The total number of factors of N = 14 * 13 * 7
We need to find the total number of even factors. For this, let us find the total number of odd factors and then subtract this from the total number of factors. Any odd factor will have to be a combination of powers of only 5 and 7.
Total number of odd factors of 213 * 512 * 76 = (12 + 1) * (6 + 1) = 13 * 7
Total number of factors = (13 + 1) * (12 + 1) * (6 + 1)
Total number of even factors = 14 * 13 * 7 - 13 * 7
Number of even factors = 13 * 13 * 7 = 1183
Answer:
1183 is the answer
Step-by-step explanation:
The prime factorization of 26 * 55 * 76 * 107 is 213 * 512 * 76.
The total number of factors of N = 14 * 13 * 7
We need to find the total number of even factors. For this, let us find the total number of odd factors and then subtract this from the total number of factors. Any odd factor will have to be a combination of powers of only 5 and 7.
Total number of odd factors of 213 * 512 * 76 = (12 + 1) * (6 + 1) = 13 * 7
Total number of factors = (13 + 1) * (12 + 1) * (6 + 1)
Total number of even factors = 14 * 13 * 7 - 13 * 7
Number of even factors = 13 * 13 * 7 = 1183
Hence the answer is 1183
Choice A is the correct answer.