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=2^5\times3^2) and (B=2^3\times3^4), what is the LCM of (A) and (B)?MediumLevel 5What are the distinct prime factors of 1155?MediumLevel 5If the HCF of two numbers is 21 and their LCM is 420, what is their product?MediumLevel 5What is the prime factorisation of 2025?MediumLevel 5Which option gives the correct statement about 1?MediumLevel 5If (p=2^2\times3\times5^2) and (q=2^3\times5\times7), what is the HCF of (p) and (q)?MediumLevel 5If (p=2^2\times3\times5^2) and (q=2^3\times5\times7), what is the LCM of (p) and (q)?MediumLevel 5Which is the prime factorisation of 1848?MediumLevel 5Which conclusion correctly follows from the Fundamental Theorem of Arithmetic?MediumLevel 5If (r=2^6\times3\times5^2), what is the value of (r)?MediumLevel 5If two numbers have no common prime factor in their prime factorisations, what will their HCF be?MediumLevel 5Which number has prime factorisation (2^4\times3\times7)?MediumLevel 5If the prime factorisation of a number is (2^3\times3^a\times5) and the number is 1080, what is the value of (a)?MediumLevel 5If (a=2^2\times3^2\times5) and (b=2\times3\times5\times7), what will be the power of 3 in the prime factorisation of (ab)?MediumLevel 5If (a=2^3\times5^2) and (b=2^2\times5^3), what will be the power of 5 in the prime factorisation of (ab)?MediumLevel 5If a number has only (2^3) and (5^2) in its prime factorisation, by which number must it be divisible?MediumLevel 5Which is the prime factorisation of 1323?MediumLevel 5If (x=2^3\times3^2) and (y=2^2\times3^3), what will be the power of 2 in (xy)?MediumLevel 5If (x=2^4\times3\times5) and (y=2^2\times3^3\times5^2), what is the HCF of (x) and (y)?MediumLevel 5According to the Fundamental Theorem of Arithmetic, which statement about prime factorisation is correct?MediumLevel 6