CBSE Class 10 Maths Standard Fundamental Theorem of Arithmetic Competency Based Questions

Topic-wise competency based questions from Real Numbers. Attempt first, then open the answer and solution.

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CBQs Important Questions PYQs

ChapterTopic

Question 1MCQ · Apply · 1 mark

Real Numbers · Fundamental Theorem of Arithmetic

If $a = 2^{3} \times 3^{2}$ , $b = 2^{2} \times 5$ , and $c = 3 \times 5^{2}$ , then $LCM (a, b, c)$ is:

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Question 2MCQ · Apply · 1 mark

Real Numbers · Fundamental Theorem of Arithmetic

The HCF of two numbers is $48$ and their LCM is $4800$ . If $LCM = 48 k$ , find $k$ .

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Question 3MCQ · Apply · 1 mark

Real Numbers · Fundamental Theorem of Arithmetic

What is the LCM of the smallest two-digit positive integer and the smallest composite number?

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Question 4MCQ · Apply · 1 mark

Real Numbers · Fundamental Theorem of Arithmetic

The sum of the exponents in the prime factorisation of $360$ is:

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Question 5MCQ · Understand · 1 mark

Real Numbers · Fundamental Theorem of Arithmetic

If $p$ is prime, how many positive factors does $p^{2}$ have?

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Question 6MCQ · Apply · 1 mark

Real Numbers · Fundamental Theorem of Arithmetic

The HCF and LCM, respectively, of $18, 24, 30$ are:

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Question 7MCQ · Understand · 1 mark

Real Numbers · Fundamental Theorem of Arithmetic

$n$ is a natural number greater than $1$ . Which expression must be writable as a product of prime numbers?

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Question 8MCQ · Understand · 1 mark

Real Numbers · Fundamental Theorem of Arithmetic

If a natural number $N$ is divisible by $30$ , its prime factorisation must include:

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Question 9MCQ · Analyse · 1 mark

Real Numbers · Fundamental Theorem of Arithmetic

If $HCF (k, 84) = 28$ , which statements must hold? (i) $28 ∣ k$ ; (ii) $84 ∣ k$ ; (iii) $k$ is even.

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Question 10MCQ · Analyse · 1 mark

Real Numbers · Fundamental Theorem of Arithmetic

If $LCM (M, 12) = 60$ , which is necessarily true?

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CBSE Class 10 Maths Standard Fundamental Theorem of Arithmetic Competency Based Questions

Topic-wise competency based questions from Real Numbers. Attempt first, then open the answer and solution.

ChapterTopic

CBSE Class 10 Maths Standard Fundamental Theorem of Arithmetic Competency Based Questions

If a=23×32, b=22×5, and c=3×52, then LCM(a,b,c) is:

The HCF of two numbers is 48 and their LCM is 4800. If LCM=48k, find k.

What is the LCM of the smallest two-digit positive integer and the smallest composite number?

The sum of the exponents in the prime factorisation of 360 is:

If p is prime, how many positive factors does p2 have?

The HCF and LCM, respectively, of 18,24,30 are:

n​ is a natural number greater than 1. Which expression must be writable as a product of prime numbers?

If a natural number N is divisible by 30, its prime factorisation must include:

If HCF(k,84)=28, which statements must hold? (i) 28∣k; (ii) 84∣k; (iii) k is even.

If LCM(M,12)=60, which is necessarily true?

CBSE Class 10 Maths Standard Fundamental Theorem of Arithmetic Competency Based Questions

If a=23×32, b=22×5, and c=3×52, then LCM(a,b,c) is:

The HCF of two numbers is 48 and their LCM is 4800. If LCM=48k, find k.

What is the LCM of the smallest two-digit positive integer and the smallest composite number?

The sum of the exponents in the prime factorisation of 360 is:

If p is prime, how many positive factors does p2 have?

The HCF and LCM, respectively, of 18,24,30 are:

n​ is a natural number greater than 1. Which expression must be writable as a product of prime numbers?

If a natural number N is divisible by 30, its prime factorisation must include:

If HCF(k,84)=28, which statements must hold? (i) 28∣k; (ii) 84∣k; (iii) k is even.

If LCM(M,12)=60, which is necessarily true?

If $a = 2^{3} \times 3^{2}$ , $b = 2^{2} \times 5$ , and $c = 3 \times 5^{2}$ , then $LCM (a, b, c)$ is:

The HCF of two numbers is $48$ and their LCM is $4800$ . If $LCM = 48 k$ , find $k$ .

The sum of the exponents in the prime factorisation of $360$ is:

If $p$ is prime, how many positive factors does $p^{2}$ have?

The HCF and LCM, respectively, of $18, 24, 30$ are:

$n$ is a natural number greater than $1$ . Which expression must be writable as a product of prime numbers?

If a natural number $N$ is divisible by $30$ , its prime factorisation must include:

If $HCF (k, 84) = 28$ , which statements must hold? (i) $28 ∣ k$ ; (ii) $84 ∣ k$ ; (iii) $k$ is even.

If $LCM (M, 12) = 60$ , which is necessarily true?

If $a = 2^{3} \times 3^{2}$ , $b = 2^{2} \times 5$ , and $c = 3 \times 5^{2}$ , then $LCM (a, b, c)$ is:

The HCF of two numbers is $48$ and their LCM is $4800$ . If $LCM = 48 k$ , find $k$ .

The sum of the exponents in the prime factorisation of $360$ is:

If $p$ is prime, how many positive factors does $p^{2}$ have?

The HCF and LCM, respectively, of $18, 24, 30$ are:

$n$ is a natural number greater than $1$ . Which expression must be writable as a product of prime numbers?

If a natural number $N$ is divisible by $30$ , its prime factorisation must include:

If $HCF (k, 84) = 28$ , which statements must hold? (i) $28 ∣ k$ ; (ii) $84 ∣ k$ ; (iii) $k$ is even.

If $LCM (M, 12) = 60$ , which is necessarily true?