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The function f(n) for an integer n is defined by the number of prime factors of n. What is the value of f(f(210 x 143))?
A. 1
B. 2
C. 3
D. 4
E. 6
A. 1
B. 2
C. 3
D. 4
E. 6
ExpertsGlobal5
f(n) is given as number of prime facrors of n, so we will have to factorize n..
f(210×143) = f((2×3×5×7)×(11×13))
Thus SIX prime factors.
So f(f(210×143))=f(6)
Now f(6) = f(2×3)
Thus answer is 2.
B
27 Apr 2026, 22:39
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We just need to count prime factors carefully.
Step 1: Factor the numbers
210 = 2 × 3 × 5 × 7
143 = 11 × 13
So,
210 × 143 = 2 × 3 × 5 × 7 × 11 × 13
---
Step 2: Evaluate f(210 × 143)
f(n) = number of prime factors
Here we have 6 distinct prime factors:
2, 3, 5, 7, 11, 13
So,
f(210 × 143) = 6
---
Step 3: Evaluate f(f(210 × 143)) = f(6)
Now factor 6:
6 = 2 × 3
So number of prime factors = 2
---
Final Answer: 2
---
Hope this helps.
If you want to look at it a different way, feel free to tag me.
– Rajdeep
Step 1: Factor the numbers
210 = 2 × 3 × 5 × 7
143 = 11 × 13
So,
210 × 143 = 2 × 3 × 5 × 7 × 11 × 13
---
Step 2: Evaluate f(210 × 143)
f(n) = number of prime factors
Here we have 6 distinct prime factors:
2, 3, 5, 7, 11, 13
So,
f(210 × 143) = 6
---
Step 3: Evaluate f(f(210 × 143)) = f(6)
Now factor 6:
6 = 2 × 3
So number of prime factors = 2
---
Final Answer: 2
---
Hope this helps.
If you want to look at it a different way, feel free to tag me.
– Rajdeep
