Advertisements
Advertisements
प्रश्न
State Fundamental Theorem of Arithmetic.
उत्तर
FUNDAMENTAL THEOREM OF ARITHMETIC:
Every composite number can be expressed (factorised) as a product of primes, and this factorization is unique except for the order in which the prime factors occur.
While writing a positive integer as the product of primes, if we decide to write the prime factors in ascending order and we combine the same primes, then the integer is expressed as the product of powers of primes and the representation is unique.
So,we can say that every composite number can be expressed as the products of powers distinct primes in ascending or descending order in a unique way.
APPEARS IN
संबंधित प्रश्न
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
Write the exponent of 2 in the price factorization of 144.
Express the number as a product of its prime factor:
3825
If two positive integers A and B can be expressed as A = xy3 and B = x4y2z; x, y being prime numbers then HCF (A, B) is ______.
The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is ______.
The ratio of LCM and HCF of the least composite and the least prime numbers is ______.
For some integer m, every even integer is of the form ______.
On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF (a, b) = pmqn and LCM (a, b) = prqs, then (m + n)(r + s) = ______.
If n is a natural number, then 8n cannot end with digit