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 (a=2^4\times3^5\times7) and (b=2^7\times3^2\times7^2), what is the power of 7 in the HCF of (a) and (b)?HardLevel 6Which is the prime factorisation of 20412?HardLevel 6If a number has prime factorisation (2^8\times3^4\times5^2), what is the smallest number by which it must be multiplied to make a perfect cube?HardLevel 6By which smallest number should 21168 be divided to get a perfect square?HardLevel 6If (x=2^5\times3^2\times7^3) and (y=2^3\times5\times7^4), what will be the power of 7 in (xy)?HardLevel 6If (x=2^7\times3^2\times5) and (y=2^6\times3\times11), what will be the power of 2 in (xy)?HardLevel 6Which option gives all distinct prime factors of 45045 correctly?HardLevel 6If (a=2^5\times3^2\times11^2) and (b=2^3\times3^4\times5\times11), what is the HCF of (a) and (b)?HardLevel 6If (a=2^5\times3^2\times11^2) and (b=2^3\times3^4\times5\times11), what is the LCM of (a) and (b)?HardLevel 6If the HCF of two numbers is 120 and their LCM is 8400, what is the power of 2 in their product?HardLevel 6If the HCF of two numbers is 66 and their LCM is 30030, what is the power of 13 in their product?HardLevel 6What is the prime factorisation of 28561?HardLevel 6If (n=2^8\times3^5\times5^6), by which smallest number should (n) be divided to make it a perfect cube?HardLevel 6Which option gives the number formed by (2^5\times3^3\times5\times7)?HardLevel 6If (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 6If two numbers have prime factorisations (2^5\times3^4) and (2^8\times3^2), what is the ratio of their LCM to HCF?HardLevel 6If (x=2^4\times3^5\times5^3) and (y=2^6\times3^2\times5^4), how many prime factors will (xy) have if repetition is counted?HardLevel 6If (m=2^6\times3^3\times5^2) and (n=2^4\times3^5\times5^4), what is the power of 5 in the LCM of (m) and (n)?HardLevel 6If (m=2^6\times3^3\times5^2) and (n=2^4\times3^5\times5^4), what is the power of 3 in the HCF of (m) and (n)?HardLevel 6What is the most accurate meaning of unique prime factorisation in the Fundamental Theorem of Arithmetic?ExpertLevel 4