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
Which is the correct prime factorisation of 443520?ExpertLevel 6If (a=2^9\times3^6\times5^4) and (b=2^6\times3^8\times7^3), what is the HCF of (a) and (b)?ExpertLevel 6If (a=2^9\times3^6\times5^4) and (b=2^6\times3^8\times7^3), which is the LCM of (a) and (b)?ExpertLevel 6If the product of two numbers is 3628800 and their HCF is 1440, what is their LCM?ExpertLevel 6If the HCF of two numbers is 420 and their LCM is 18480, what is their product?ExpertLevel 6What is the smallest positive number by which 86400 must be multiplied to get a perfect square?ExpertLevel 6By which smallest number should 105840 be divided to get a perfect square?ExpertLevel 6What is the smallest number by which 60480 must be multiplied to get a perfect cube?ExpertLevel 6What is the prime factorisation of 1000188?ExpertLevel 6If (N=2^{13}\times3^8\times5^5\times7^2), by which smallest number must (N) be multiplied to make it a perfect square?ExpertLevel 6If (N=2^{11}\times3^8\times5^5\times7^2), by which smallest number must (N) be multiplied to make it a perfect cube?ExpertLevel 6If (a=2^8\times3^7\times5^3) and (b=2^6\times3^9\times7^2), what will be the power of 3 in (ab)?ExpertLevel 6If (x=2^{10}\times3^5\times5^8) and (y=2^7\times5^6\times11^3), what will be the power of 5 in (xy)?ExpertLevel 6If (A=2^{13}\times3^9\times5^5) and (B=2^{10}\times3^{11}\times7^4), which is the HCF of (A) and (B)?ExpertLevel 6If (A=2^{13}\times3^9\times5^5) and (B=2^{10}\times3^{11}\times7^4), which is the LCM of (A) and (B)?ExpertLevel 6The HCF of two numbers is 180 and their LCM is 27720. If one number is 1260, what is the other number?ExpertLevel 6The HCF of two numbers is 216 and their LCM is 30240. If one number is 1512, what is the other number?ExpertLevel 6If (p=2^a\times3^4\times5\times7) and (p=90720), what is the value of (a)?ExpertLevel 6If (q=2^7\times3^b\times5^2\times7) and (q=3628800, what is the value of (b)?ExpertLevel 6If a number has prime factorisation (2^{10}\times3^8\times5^7\times19^2), how many prime factors are there if repetition is counted?ExpertLevel 6