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divisible factors MCQ Questions for Class 10

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2 questions tagged with divisible factors.

Question 1/2 Expert Mathematics Chapter 1: Real Numbers 3: Prime factorisation Class 10 Level 7

किसी संख्या का अभाज्य गुणनखंड रूप \(2^3\times3^2\times5^4\) है। उसमें (5) से विभाज्य गुणनखंडों की संख्या कितनी है?

A number has prime factorisation \(2^3\times3^2\times5^4\). How many of its factors are divisible by (5)?

Explanation opens after your attempt
Correct Answer

A. (48)

Step 1

Concept

A factor divisible by (5) must have power of (5) at least (1).

Step 2

Why this answer is correct

Choices are (4) for (2), (3) for (3), and (4) for (5). Total \(=4\times3\times4=48\).

Step 3

Exam Tip

Do not include zero power for the required prime. चरण 1: (5) से विभाज्य गुणनखंड में (5) की घात कम से कम (1) होगी। चरण 2: (2) के लिए (4) तरीके, (3) के लिए (3) तरीके, और (5) के लिए (1,2,3,4) यानी (4) तरीके। कुल \(4\times3\times4=48\)। चरण 3: शर्त वाले अभाज्य की शून्य घात को शामिल न करें।

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Question 2/2 Expert Mathematics Chapter 1: Real Numbers 3: Prime factorisation Class 10 Level 7

यदि \(2520=2^3\times3^2\times5\times7\), तो (2520) के ऐसे धनात्मक गुणनखंडों की संख्या कितनी है जो (2) से विभाज्य हैं?

If \(2520=2^3\times3^2\times5\times7\), how many positive factors of (2520) are divisible by (2)?

Explanation opens after your attempt
Correct Answer

A. (36)

Step 1

Concept

A factor divisible by (2) must contain \(2^1\) at least.

Step 2

Why this answer is correct

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

Exam Tip

For conditional factors, adjust only the restricted prime exponent. चरण 1: (2) से विभाज्य गुणनखंड में (2) की घात कम से कम (1) होनी चाहिए। चरण 2: (2) की घात (1,2,3) यानी (3) तरीके; (3) के लिए (3) तरीके; (5) और (7) के लिए (2-2) तरीके। कुल \(3\times3\times2\times2=36\)। चरण 3: शर्त वाले गुणनखंडों में उस अभाज्य की घात की सीमा ध्यान से बदलें।

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