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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

Which is the prime factorisation of 35280?If (27720=2^a\times3^2\times5\times7\times11), what is the value of (a)?If (31104=2^7\times3^b), what is the value of (b)?If (19600=2^4\times5^m\times7^2), what is the value of (m)?If (20790=2\times3^p\times5\times7\times11), what is the value of (p)?Which number has prime factorisation (2^3\times3^2\times7\times11)?Which number has prime factorisation (2^5\times3^3\times7)?Which number has prime factorisation (3^2\times5^2\times7^2)?Which number has prime factorisation (2^4\times3\times5\times7^2)?Which number has prime factorisation (2^7\times3^5)?If the number is (2^5\times3^4\times5^2\times7), by which smallest number should it be multiplied to make a perfect square?If the number is (2^4\times3^5\times5^2), by which smallest number should it be divided to make a perfect square?If the number is (2^4\times3^2\times5^3\times7), by which smallest number should it be multiplied to make a perfect cube?If the number is (2^8\times3^5\times5^4\times11^2), by which smallest number should it be divided to make a perfect cube?If (n=2^6\times3^4\times5^2\times7), by which number will (n) not be divisible?If (n=2^8\times3^3\times5^5), by which number must (n) be divisible?If a number has prime factorisation (2^4\times3^2\times5^2\times7^2), how many prime factors does it have if repetition is counted?If a number has prime factorisation (2^7\times3^5\times11^2\times13), how many distinct prime factors does it have?If (a=2^5\times3^2\times7) and (b=2^3\times3^4\times5), what will be the power of 3 in (ab)?If (x=2^8\times5^3\times11) and (y=2^4\times3^2\times5^5), what will be the power of 5 in (xy)?