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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
Consider the number 12n where n is a natural number. Check whether there is any value of n ∈ N for which 12n ends with the digital zero.
Consider the number 6n where n is a natural number. Check whether there is any value of n ∈ N for which 6n is divisible by 7.
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 the following positive integer:
45470971
Express the number as a product of its prime factor:
156
Express the number as a product of its prime factor:
3825
Express the number as a product of its prime factor:
5005
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510 and 92
If m, n are natural numbers, for what values of m, does 2n × 5m ends in 5?
Find the H.C.F. of 252525 and 363636
What is the smallest number that when divided by three numbers such as 35, 56 and 91 leaves remainder 7 in each case?
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 ______.
n2 – 1 is divisible by 8, if n is ______.
Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.
The LCM of smallest 2-digit number and smallest composite number is ______.
Read the following passage:
|
Khushi wants to organize her birthday party. Being health conscious, she decided to serve only fruits in her birthday party. She bought 36 apples and 60 bananas and decided to distribute fruits equally among all. |
Based on the above information, answer the following questions:
- How many guests Khushi can invite at the most?
- How many apples and bananas will each guest get?
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- If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
OR - If the cost of 1 dozen of bananas is ₹ 60, the cost of 1 apple is ₹ 15 and cost of 1 mango is ₹ 20, find the total amount spent on 60 bananas, 36 apples and 42 mangoes.
- If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
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The prime factorisation of the number 5488 is ______.
If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is ______.
The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is ______.
