$CATEGORY: Maths - TicTacLearn/1. Real Numbers/1. Real Numbers--The Fundamental Theorem of Arithmetic

//Multiple Choice

The fundamental theorem of arithmetic is also called as {
~ Composite Theorem
~ Euclid Theorem
= Unique Factorisation Theorem
~ None of the above
}

As per Fundamental Theorem of Arithmetic, the number  13915 is a {
= Composite number
~ Prime number
~ Even number
~ None of the above
}

The HCF of 34, 39, 91 is {
= 1
~ 13
~ 3
~ None of the above
}

The LCM and HCF of 816 and 170 , using the fundamental theorem of arithmetic is {
= LCM\= 4080 and HCF\= 34
~ LCM\= 3500 and HCF\=17
~ LCM\=2090 and HCF\= 1
~ None of the above
}

Find the value of n ( where n is a natural number) for which \(4^n\) ends with the digit zero. {
= There is no natural number n for which \(4^n\) ends with the digit zero.
~ There is a natural number n for which \(4^n\) ends with the digit zero.
~ There is a prime number n for which \(4^n\) ends with the digit zero.
~ None of the above
}

//True or False

The number 9  is prime number {F}

The LCM of 135 and 24 is 1,080 {T}

The HCF  of 21 and 90 is 1 {F}

The LCM of two numbers is 7991 and the two numbers are 61 and 131. Their HCF is 1 {T}

A bakery sells cookies in three boxes. The three boxes contain 60, 84 and 108 numbers of cookies. The baker wants to sells all the cookies in any of the three boxes. The least number of cookies that he can bake, in a day, so that he is able to sell all his cookies in any of the three boxes is 3,780 {T}

Two buckets contain 546 and 764 liters of water respectively. The maximum capacity of a container which can measure the water of either buckets exact number of times is 108 litres {F}

A number in the form of 6n, where n belongs to natural numbers, can never end with the digit 0 {T}



//Fill in the blanks

___ is the HCF of 80 and 567 is {
~ 80
~ 567
= 1
~ None of the above
}

If the HCF of two numbers is 1 and the LCM is 3395. _____is the other number if one of them is 97. {
~ 40
~ 30
~ 45
= 35
}

If a number cannot be expressed in the form p /q where p and q are integers and q is not equal to  zero , then it is called an _____ {
= Irrational number
~ Rational number
~ Whole number
~ Prime number
}

If a number can be expressed in the form p /q where p and q are integers and q is not equal to zero, then it is called _____ {
~ Irrational number
= Rational number
~ Whole number
~ Prime number
}

The fundamental theorem of arithmetic, is the process of expressing a natural number as a _____ of prime numbers known as prime factorization. {
~ Sum of prime numbers
= Product of Prime numbers
~ Sum and product of prime number
~ None of the above
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=HCF× LCM\= -> Product of two natural  numbers
=LCM (12,8) × HCF (12,8) \= -> 96
=HCF of 25,35,45 -> 5
=LCM of 6,8, 12 -> 24
}


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