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 two numbers have no common prime factor in their prime factorisations, what are they called?MediumLevel 6Which number has prime factorisation (2^5\times3\times7)?MediumLevel 6If the prime factorisation of a number is (2^4\times3^a\times5) and the number is 6480, what is the value of (a)?MediumLevel 6If (a=2^3\times3^2\times5) and (b=2^2\times3\times5^2), what will be the power of 5 in the prime factorisation of (ab)?MediumLevel 6If (a=2^4\times7^2) and (b=2^3\times7), what will be the power of 7 in the prime factorisation of (ab)?MediumLevel 6If a number has (2^2), (3), and (5) in its prime factorisation, by which number must it be divisible?MediumLevel 6Which is the prime factorisation of 3087?MediumLevel 6If (x=2^5\times3^2) and (y=2^3\times3^4), what will be the power of 2 in (xy)?MediumLevel 6If (x=2^5\times3^2\times5) and (y=2^3\times3^4\times5^2), what is the HCF of (x) and (y)?MediumLevel 6According to the Fundamental Theorem of Arithmetic, if two different prime factorisations of a number seem to appear, what is the correct conclusion?HardLevel 4Which is the prime factorisation of 27720?HardLevel 4If (a=2^4\times3^3\times5^2) and (b=2^2\times3^5\times7), what is the HCF of (a) and (b)?HardLevel 4If (a=2^4\times3^3\times5^2) and (b=2^2\times3^5\times7), what is the LCM of (a) and (b)?HardLevel 4If the product of two numbers is 60480 and their HCF is 72, what is their LCM?HardLevel 4If the HCF of two numbers is 45 and their LCM is 1260, what is their product?HardLevel 4What is the smallest positive number by which 1800 must be multiplied to get a perfect square?HardLevel 4By which smallest number should 8820 be divided to get a perfect square?HardLevel 4What is the smallest number by which 5400 must be multiplied to get a perfect cube?HardLevel 4What is the prime factorisation of 9261?HardLevel 4If (N=2^5\times3^4\times5^2\times7), by which smallest number must (N) be multiplied to make it a perfect square?HardLevel 4