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 prime factorisation of 110880?ExpertLevel 4If (a=2^7\times3^4\times5^3) and (b=2^4\times3^6\times7^2), what is the HCF of (a) and (b)?ExpertLevel 4If (a=2^7\times3^4\times5^3) and (b=2^4\times3^6\times7^2), what is the LCM of (a) and (b)?ExpertLevel 4If the product of two numbers is 907200 and their HCF is 360, what is their LCM?ExpertLevel 4If the HCF of two numbers is 126 and their LCM is 4620, what is their product?ExpertLevel 4What is the smallest positive number by which 43200 must be multiplied to get a perfect square?ExpertLevel 4By which smallest number should 26460 be divided to get a perfect square?ExpertLevel 4What is the smallest number by which 15120 must be multiplied to get a perfect cube?ExpertLevel 4What is the prime factorisation of 250047?ExpertLevel 4If (N=2^9\times3^6\times5^5\times11^3), by which smallest number must (N) be multiplied to make it a perfect square?ExpertLevel 4If (N=2^8\times3^7\times5^4\times7^2), by which smallest number must (N) be multiplied to make it a perfect cube?ExpertLevel 4If (a=2^6\times3^5\times7^2) and (b=2^4\times3^7\times5^3), what will be the power of 3 in (ab)?ExpertLevel 4If (x=2^7\times3^3\times5^6) and (y=2^5\times5^4\times11^2), what will be the power of 5 in (xy)?ExpertLevel 4If (A=2^{11}\times3^7\times5^3) and (B=2^8\times3^9\times7^4), which is the HCF of (A) and (B)?ExpertLevel 4If (A=2^{11}\times3^7\times5^3) and (B=2^8\times3^9\times7^4), which is the LCM of (A) and (B)?ExpertLevel 4The HCF of two numbers is 84 and their LCM is 4620. If one number is 420, what is the other number?ExpertLevel 4The HCF of two numbers is 96 and their LCM is 6720. If one number is 480, what is the other number?ExpertLevel 4If (p=2^a\times3^4\times5\times7) and (p=45360), what is the value of (a)?ExpertLevel 4If (q=2^5\times3^b\times5^2\times7) and (q=604800), what is the value of (b)?ExpertLevel 4If a number has prime factorisation (2^8\times3^6\times5^5\times13^2), how many prime factors are there if repetition is counted?ExpertLevel 4