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If (N=2^a \times 3^b) has (20) total factors and (a=4), what is the value of (b)?
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Answer and explanation
Correct answer: 3
Step 1: The total number of factors is ((a+1)(b+1)). Step 2: With (a=4), (5(b+1)=20), so (b+1=4) and (b=3). Step 3: Make an equation when finding an exponent from factor count.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Step 1: The total number of factors is ((a+1)(b+1)). Step 2: With (a=4), (5(b+1)=20), so (b+1=4) and (b=3). Step 3: Make an equation when finding an exponent from factor count.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Prime Factorisation.
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