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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 (a=2^r\times3^2) has (15) positive factors, what is the value of (r)?Which smallest number should be multiplied by (2^3\times3^2\times5) to get a perfect square?If (p=2^2\times3\times11) and (q=2\times3^3\times11^2), what is the ratio of HCF to LCM of (p) and (q)?If the prime factorisation of (420) is (2^2\times3\times5\times7), how many even factors does (420) have?Which option gives the correct prime factorisation of (990)?If (k=2^3\times3^2\times5^2\times7), how many factors of (k) are divisible by (15)?If (N=2^a\times3^b) and (N) has (18) total factors, which pair is possible?If (A=2^4\times3^2\times5) and (B=2^2\times3\times5^3), how many times is their LCM greater than their HCF?If (2^3\times3^x\times5^2) is a perfect square, which value of (x) is not possible?If (2^x\times3^2\times7^4) has (45) total factors, what is the value of (x)?Which option gives the correct prime factorisation of (1260)?If (180=2^2\times3^2\times5), how many factors of (180) are perfect squares?If (540=2^2\times3^3\times5), how many factors of (540) are perfect cubes?If (a=2^3\times3\times5) and (b=2^2\times3^2\times5^2), what is the prime factorised form of (a\times b)?If (a=2^6\times3^4\times5^2) and (b=2^2\times3\times5), what is the prime factorised form of (\frac{a}{b})?A number has prime factorisation (2^3\times3^2\times5^4). How many of its factors are divisible by (5)?If (N=2^2\times3^3\times5\times7^2), how many positive factors does (N) have?By which smallest number should (2^2\times3^4\times5^5) be divided to obtain a perfect cube?If (2^3\times3^2\times5^x) has (96) total factors, what is the value of (x)?If the HCF of two numbers is (12) and their LCM is (180), what is the prime factorised form of their product?