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=2^7\times3^5\times5^4), by which smallest number must (N) be multiplied to make it a perfect cube?HardLevel 6If (a=2^5\times3^4\times7^2) and (b=2^2\times3^6\times5), what will be the power of 3 in (ab)?HardLevel 6If (x=2^4\times3^2\times5^5) and (y=2^3\times5^2\times11), what will be the power of 5 in (xy)?HardLevel 6If (A=2^{10}\times3^6\times5^2) and (B=2^7\times3^8\times7^3), which is the HCF of (A) and (B)?HardLevel 6If (A=2^{10}\times3^6\times5^2) and (B=2^7\times3^8\times7^3), which is the LCM of (A) and (B)?HardLevel 6The HCF of two numbers is 48 and their LCM is 3360. If one number is 240, what is the other number?HardLevel 6The HCF of two numbers is 72 and their LCM is 2520. If one number is 360, what is the other number?HardLevel 6If (p=2^a\times3^3\times5\times7) and (p=7560), what is the value of (a)?HardLevel 6If (q=2^4\times3^b\times5\times7) and (q=15120), what is the value of (b)?HardLevel 6If a number has prime factorisation (2^7\times3^5\times5^4\times11), how many prime factors are there if repetition is counted?HardLevel 6If a number has prime factorisation (2^8\times3^5\times5^2\times11^3), how many distinct prime factors does it have?HardLevel 6If the two numbers are (2^6\times3^2) and (5^3\times7^2), which statement about them is correct?HardLevel 6If the product of two co-prime numbers is 2431, what is their LCM?HardLevel 6What is the prime factorisation of 16384?HardLevel 6Which is the prime factorisation of 44100?HardLevel 6If (n=2^5\times3^4\times5\times13), by which number must (n) be divisible?HardLevel 6If (n=2^6\times3^2\times5^2), by which of the following will (n) not be divisible?HardLevel 6Which option gives the correct value of (2^8\times3^3\times5)?HardLevel 6If the prime factorisation of a number is (2^4\times3^5\times5^3), what is the number?HardLevel 6If (a=2^4\times3^5\times7) and (b=2^7\times3^2\times7^2), what is the power of 2 in the LCM of (a) and (b)?HardLevel 6