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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 the number is (2^8\times3^5\times5^2\times7^3), by which smallest number should it be multiplied to make a perfect square?If the number is (2^9\times3^4\times5^7\times11^2), by which smallest number should it be divided to make a perfect square?If the number is (2^5\times3^7\times5^4\times13^2), by which smallest number should it be multiplied to make a perfect cube?If the number is (2^{10}\times3^8\times5^5\times7^4), by which smallest number should it be divided to make a perfect cube?If (n=2^8\times3^6\times5^4\times11^2), by which number will (n) not be divisible?If (n=2^{10}\times3^5\times7^4\times13^2), by which number must (n) be divisible?If a number has prime factorisation (2^9\times3^7\times5^4\times7^3\times11^2), how many prime factors does it have with repetition?If a number has prime factorisation (2^6\times3^5\times7^4\times11^3\times13^2), how many distinct prime factors does it have?If (a=2^6\times3^4\times5^2\times11) and (b=2^3\times3^5\times7\times11^2), what will be the power of 3 in (ab)?If (x=2^8\times5^3\times7^2\times13) and (y=2^5\times3^2\times5^4\times13^3), what will be the power of 13 in (xy)?Which option gives the correct value of (2^5\times3^4\times7^2)?Which option gives the correct value of (2^3\times3^5\times7^2)?Which option gives only the final prime factorisation?Which option has incomplete prime factorisation?If (2^6\times3^3\times5^2) is the prime factorisation of a number, what is the number?If (2^2\times3^2\times5^2\times11^2) is the prime factorisation of a number, what is the number?What is the correct prime factorisation of 158760?Which is the prime factorisation of 217800?What is the correct prime factorisation of 279936?Why will (8\times27225) not be considered the final answer in prime factorisation?