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प्रश्न
State fundamental theorem of arithmetic?
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उत्तर
The fundamental theorem of arithmetic, states that every integer greater than 1 either is prime itself or is the product of prime numbers, and this product is unique.
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संबंधित प्रश्न
Express the number as a product of its prime factor:
140
A merchant has 120 liters of oil of one kind, 180 liters of another kind and 240 liters of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?
Find the LCM and HCF of the following integers by applying the prime factorisation method:
24, 15 and 36
Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where, m, n are non-negative integers.\[\frac{13}{125}\]
Express the number as a product of its prime factor:
5005
Find the LCM and HCF of the following integers by applying the prime factorisation method.
8, 9 and 25
For what value of natural number n, 4n can end with the digit 6?
If p1x1 × p2x2 × p3x3 × p4x4 = 113400 where p1, p2, p3, p4 are primes in ascending order and x1, x2, x3, x4, are integers, find the value of p1, p2, p3, p4 and x1, x2, x3, x4
Find the L.C.M. and H.C.F. of 408 and 170 by applying the fundamental theorem of Arithmetic
Find the greatest number consisting of 6 digits which is exactly divisible by 24, 15, 36?
If two positive integers A and B can be expressed as A = xy3 and B = xiy2z; x, y being prime numbers, the LCM (A, B) is ______.
The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is ______.
If LCM(x, 18) = 36 and HCF(x, 18) = 2, then x is ______.
n2 – 1 is divisible by 8, if n is ______.
Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340.
Statement R (Reason): HCF is always a factor of LCM.
Assertion (A): The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.
Reason(R): For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.
If HCF (72, 120) = 24, then LCM (72, 120) is ______.
The prime factorisation of the number 2304 is ______.
National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same artform and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room?
