Advertisements
Advertisements
प्रश्न
State fundamental theorem of arithmetic?
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
What is the HCF of the smallest prime number and the smallest composite number?
Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.
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?
Determine the prime factorisation of each of the following positive integer:
45470971
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.\[\frac{13}{125}\]
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.\[\frac{129}{2^2 \times 5^7}\]
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?
For some integer p, every even integer is of the form ______.
When a number is divided by 7, its remainder is always ______.
If LCM(x, 18) = 36 and HCF(x, 18) = 2, then x is ______.
n2 – 1 is divisible by 8, if n is ______.
If two positive integers a and b are written as a = x3 y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is ______.
Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.
Show that 12n cannot end with the digit 0 or 5 for any natural number n.
Find the HCF and LCM of 26, 65 and 117, using prime factorisation.
The LCM of smallest 2-digit number and smallest composite number is ______.
(HCF × LCM) for the numbers 30 and 70 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?
