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=2^2\times3^3\times5) and (b=2^4\times3\times5^2), what is the power of 5 in the HCF of (a) and (b)?HardLevel 4Which is the prime factorisation of 3969?HardLevel 4If a number has prime factorisation (2^5\times3^2\times5^4), what is the smallest number by which it must be multiplied to make a perfect cube?HardLevel 4By which smallest number should 3528 be divided to get a perfect square?HardLevel 4If (x=2^4\times3^2\times7) and (y=2^2\times3^3\times5), what will be the power of 3 in (xy)?HardLevel 4If (x=2^5\times3\times5^2) and (y=2^3\times3^4\times5), what will be the power of 2 in (xy)?HardLevel 4Which option gives all distinct prime factors of 2310 correctly?HardLevel 4If (a=2^3\times3^2\times11) and (b=2^2\times3\times5\times11^2), what is the HCF of (a) and (b)?HardLevel 4If (a=2^3\times3^2\times11) and (b=2^2\times3\times5\times11^2), what is the LCM of (a) and (b)?HardLevel 4If the HCF of two numbers is 36 and their LCM is 900, what is the power of 2 in their product?HardLevel 4If the HCF of two numbers is 30 and their LCM is 2310, what is the power of 11 in their product?HardLevel 4What is the prime factorisation of 2401?HardLevel 4If (n=2^2\times3^5\times5^3), by which smallest number should (n) be divided to make it a perfect cube?HardLevel 4Which option gives the number formed by (2^3\times3^2\times5\times7)?HardLevel 4If (a=2^4\times3^2\times5) and (b=2^3\times3\times5^2), the product of their HCF and LCM will be equal to what?HardLevel 4If two numbers have prime factorisations (2^3\times3^2) and (2^5\times3), what is the ratio of their LCM to HCF?HardLevel 4If (x=2^2\times3^3\times5) and (y=2^4\times3\times5^2), how many prime factors will (xy) have if repetition is counted?HardLevel 4If (m=2^5\times3^2\times7) and (n=2^2\times3^4\times7^3), what is the power of 7 in the LCM of (m) and (n)?HardLevel 4If (m=2^5\times3^2\times7) and (n=2^2\times3^4\times7^3), what is the power of 3 in the HCF of (m) and (n)?HardLevel 4In the Fundamental Theorem of Arithmetic, prime factorisation of a number is called unique. What does this correctly mean?HardLevel 5