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Subjects

Mathematics

Prime Factorisation

अभाज्य गुणनखंडन

In Class 10 Mathematics, under the Real Numbers chapter, Prime Factorisation teaches students to express a composite number as a product of prime numbers. Students practise identifying prime factors and writing factorisations using multiplication and exponents. This foundational skill supports the Fundamental Theorem of Arithmetic and later work with HCF and LCM.

Practice questions

If (N=2^3\times3^2\times5), what is the total number of positive factors of (N)?What is the smallest number by which (2^4\times3^3\times5^2) should be divided to get a perfect square?What is the smallest number by which (2^5\times3^2\times7) should be multiplied to make it a perfect cube?If two numbers have prime factorisations (2^3\times3^2\times5) and (2^2\times3^4\times7), what is their HCF?If two numbers have prime factorisations (2^3\times5^2) and (2\times3^2\times5), what is their LCM?If (a=2^4\times3\times5^2) and (b=2^2\times3^3\times5), what is the value of (\frac{\operatorname{LCM}(a,b)}{\operatorname{HCF}(a,b)})?Which number has the prime factorisation (2^2\times3\times7^2)?If a number has prime factorisation (2^a\times3^2\times5) and it has (24) total factors, what is the value of (a)?If (2520=2^3\times3^2\times5\times7), how many positive factors of (2520) are divisible by (2)?If (360=2^3\times3^2\times5), how many factors of (360) are odd?If the product of two coprime numbers is (2^4\times3^2\times5), what is their HCF?Which statement correctly describes the uniqueness of prime factorisation?If a number has prime factorisation (2^6\times3^4\times5^2), what is its square root?If a number has prime factorisation (2^9\times3^6\times7^3), what is its cube root?If (x=2^2\times3^3\times5), what is the smallest multiplier that makes (x) a perfect square?If (y=2^4\times3^5\times11^2), by what smallest number should (y) be divided to make it a perfect cube?If the HCF of two numbers is (2^2\times3) and their LCM is (2^5\times3^3\times5), what is the prime factorised form of their product?Which option gives the correct prime factorisation of (756)?If (m=2^3\times3^2\times5^2), how many factors of (m) are divisible by (10)?If (n=2^5\times3^4\times7), how many factors of (n) are not divisible by (6)?