If (2520=2^3\times3^2\times5\times7), how many positive factors of (2520) are divisible by (2)?
Answer and explanation
Correct answer: (36)
Step 1: A factor divisible by (2) must contain (2^1) at least. Step 2: Powers of (2) can be (1,2,3), giving (3) choices; powers of (3) give (3) choices; (5) and (7) give (2) choices each. Total (=3\times3\times2\times2=36). Step 3: For conditional factors, adjust only the restricted prime exponent.
Frequently asked questions
What is the correct answer to this question?
(36)
Why is this the correct answer?
Step 1: A factor divisible by (2) must contain (2^1) at least. Step 2: Powers of (2) can be (1,2,3), giving (3) choices; powers of (3) give (3) choices; (5) and (7) give (2) choices each. Total (=3\times3\times2\times2=36). Step 3: For conditional factors, adjust only the restricted prime exponent.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Prime Factorisation.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
