Mathematics
Fundamental Theorem of Arithmetic
अंकगणित का मौलिक प्रमेय
In this Class 10 Mathematics topic from the chapter Real Numbers, students learn that every integer greater than 1 can be expressed as a product of prime numbers, and that this prime factorisation is unique apart from the order of the factors. They practise finding prime factors and use the theorem to understand and determine the HCF and LCM of numbers. The topic builds clear reasoning about the structure of whole numbers and supports later work with divisibility and number relationships.
Practice questions
If the HCF of two numbers is 42 and their LCM is 30030, what is the power of 13 in their product?HardLevel 5What is the prime factorisation of 14641?HardLevel 5If (n=2^5\times3^4\times7^3), by which smallest number should (n) be divided to make it a perfect cube?HardLevel 5Which option gives the number formed by (2^4\times3^3\times5\times7)?HardLevel 5If (a=2^5\times3^2\times5) and (b=2^3\times3^4\times5^2), the product of their HCF and LCM will be equal to what?HardLevel 5If two numbers have prime factorisations (2^4\times3^3) and (2^7\times3), what is the ratio of their LCM to HCF?HardLevel 5If (x=2^3\times3^4\times5^2) and (y=2^5\times3^2\times5^3), how many prime factors will (xy) have if repetition is counted?HardLevel 5If (m=2^6\times3^3\times7^2) and (n=2^4\times3^5\times7^4), what is the power of 7 in the LCM of (m) and (n)?HardLevel 5If (m=2^6\times3^3\times7^2) and (n=2^4\times3^5\times7^4), what is the power of 3 in the HCF of (m) and (n)?HardLevel 5What does uniqueness of prime factorisation in the Fundamental Theorem of Arithmetic clarify?HardLevel 6Which is the prime factorisation of 83160?HardLevel 6If (a=2^6\times3^5\times5^3) and (b=2^4\times3^7\times7^2), what is the HCF of (a) and (b)?HardLevel 6If (a=2^6\times3^5\times5^3) and (b=2^4\times3^7\times7^2), what is the LCM of (a) and (b)?HardLevel 6If the product of two numbers is 362880 and their HCF is 144, what is their LCM?HardLevel 6If the HCF of two numbers is 63 and their LCM is 4620, what is their product?HardLevel 6What is the smallest positive number by which 10800 must be multiplied to get a perfect square?HardLevel 6By which smallest number should 13230 be divided to get a perfect square?HardLevel 6What is the smallest number by which 7560 must be multiplied to get a perfect cube?HardLevel 6What is the prime factorisation of 74088?HardLevel 6If (N=2^7\times3^5\times5^4\times11^2), by which smallest number must (N) be multiplied to make it a perfect square?HardLevel 6