If integer k is equal to the sum of all even multiples of 15 between 295 and 615, what is the greatest prime factor of k?
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Answer:
greatest prime factor of k = 11
Step-by-step explanation:
If integer k is equal to the sum of all even multiples of 15 between 295 and 615
even multiples of 15 between 295 and 615
300 , 330 , 360 , ........................................., 570 , 600
This is an AP where
a = 300
d = 30
L = 600
600 = 300 + (n-1)30
=> n-1 = 10
=> n = 11
Number of terms = 11
Sum = (n/2)(a + L)
k = (11/2)(300 + 600)
k = 11 * 450
k = 11 * ( 2 * 3 * 3 * 5 * 5)
greatest prime factor of k = 11
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