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 number has prime factorisation (2^8\times3^5\times11^2), how many distinct prime factors does it have?HardLevel 5If the two numbers are (2^4\times3^2) and (5^3\times7), which statement about them is correct?HardLevel 5If the product of two co-prime numbers is 1547, what is their LCM?HardLevel 5What is the prime factorisation of 8192?HardLevel 5Which is the prime factorisation of 14700?HardLevel 5If (n=2^4\times3^3\times5\times11), by which number must (n) be divisible?HardLevel 5If (n=2^4\times3^2\times5), by which of the following will (n) not be divisible?HardLevel 5Which option gives the correct value of (2^7\times3^2\times5)?HardLevel 5If the prime factorisation of a number is (2^4\times3^5\times5^2), what is the number?HardLevel 5If (a=2^3\times3^5\times7) and (b=2^6\times3^2\times7^2), what is the power of 2 in the LCM of (a) and (b)?HardLevel 5If (a=2^3\times3^5\times7) and (b=2^6\times3^2\times7^2), what is the power of 3 in the HCF of (a) and (b)?HardLevel 5Which is the prime factorisation of 15876?HardLevel 5If a number has prime factorisation (2^7\times3^5\times5^4), what is the smallest number by which it must be multiplied to make a perfect cube?HardLevel 5By which smallest number should 6615 be divided to get a perfect square?HardLevel 5If (x=2^5\times3^3\times7) and (y=2^2\times3^4\times5), what will be the power of 3 in (xy)?HardLevel 5If (x=2^6\times3^2\times5^3) and (y=2^4\times3^5\times5), what will be the power of 2 in (xy)?HardLevel 5Which option gives all distinct prime factors of 30030 correctly?HardLevel 5If (a=2^4\times3^3\times13) and (b=2^2\times3\times5\times13^2), what is the HCF of (a) and (b)?HardLevel 5If (a=2^4\times3^3\times13) and (b=2^2\times3\times5\times13^2), what is the LCM of (a) and (b)?HardLevel 5If the HCF of two numbers is 72 and their LCM is 1800, what is the power of 3 in their product?HardLevel 5