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 (N=2^4\times3^5\times5^2), by which smallest number must (N) be multiplied to make it a perfect cube?HardLevel 4If (a=2^3\times3^2\times5) and (b=2^2\times3^4\times7), what will be the power of 3 in (ab)?HardLevel 4If (x=2^6\times3^3\times5) and (y=2^2\times3^5\times5^4), what will be the power of 5 in (xy)?HardLevel 4If (A=2^8\times3^4\times5^2) and (B=2^5\times3^6\times7), what is the HCF of (A) and (B)?HardLevel 4If (A=2^8\times3^4\times5^2) and (B=2^5\times3^6\times7), which is the LCM of (A) and (B)?HardLevel 4The HCF of two numbers is 18 and their LCM is 540. If one number is 90, what is the other number?HardLevel 4The HCF of two numbers is 24 and their LCM is 840. If one number is 120, what is the other number?HardLevel 4If (p=2^a\times3^2\times5) and (p=720), what is the value of (a)?HardLevel 4If (q=2^3\times3^b\times7) and (q=1512), what is the value of (b)?HardLevel 4If a number has prime factorisation (2^4\times3^3\times5^2), how many prime factors are there if repetition is counted?HardLevel 4If a number has prime factorisation (2^6\times3^2\times7^3), how many distinct prime factors does it have?HardLevel 4If the two numbers are (2^5\times3) and (5^2\times7), which statement is correct about them?HardLevel 4If the product of two co-prime numbers is 1001, what is their LCM?HardLevel 4What is the prime factorisation of 4096?HardLevel 4Which is the prime factorisation of 11025?HardLevel 4If (n=2^3\times3^2\times5\times7), by which number must (n) be divisible?HardLevel 4If (n=2^4\times3\times5^2), by which of the following will (n) not be divisible?HardLevel 4Which option gives the correct value of (2^6\times3^2\times5)?HardLevel 4If the prime factorisation of a number is (2^3\times3^4\times5^2), what is the number?HardLevel 4If (a=2^2\times3^3\times5) and (b=2^4\times3\times5^2), what is the power of 2 in the LCM of (a) and (b)?HardLevel 4