Question 1156615: FIND THE NUMBER OF DIVISORS OF 1050. SHOW ALL WORK.
SOLVE. P(n,3)=24C(n,4)
Answer by greenestamps(13203)   (Show Source):
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Number of divisors of 1050....
(1) Find the prime factorization of 1050: (2^1)(3^1)(5^2)(7^1)
(2) Add one to each exponent and multiply: 2*2*3*2 = 24
The number of divisors of 1050 is 24.
Explanation....
Given the prime factorization of 1050, every divisor of 1050 can contain only prime factors of 2, 3, 5, and/or 7. When building a factor of 1050 from the prime factorization, there are...
2 choices for the number of factors of 2 (0 or 1)
2 choices for the number of factors of 3 (0 or 1)
3 choices for the number of factors of 5 (0, 1, or 2)
2 choices for the number of factors of 7 (0 or 1)
The total number of ways to build a divisor of 1050 is then 2*2*3*2.
Solve P(n,3) = 24C(n,4)....
Cancel the common factors n, n-1, and n-2:
ANSWER: n=4
CHECK:
P(4,3) = 4*3*2 = 24
24C(4,4) = 24*1 = 24
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