$$Smallest$$ $$\Pr ime$$ $$\ Number$$

$$2$$ As 1 is neither a prime nor a composite number

$$Smallest$$ $$Composite$$ $$\ Number$$

$$4$$ As 2 and 3 are Prime numbers

$$Smallest$$ $$Odd\ Composite$$ $$Number$$

$$9$$ As 3, 5 and 7 are Prime numbers and 1 is neither a Prime nor a Composite number.

$$9\ and\ 14\ are$$ Co-Prime Numbers $$True\ or\ False$$

$$True$$ $$9=3\times3$$ $$8=2\times2\times2$$ No common factor, hence Co-Prime

Prime numbers have more than two factors $$True\ or\ False$$

$$False$$ They have only two factors: 1 and the number itself

The product of two irrational numbers can never be a rational number. $$True\ or\ False$$

$$False$$ $$\sqrt[]{2}\times\sqrt[]{8}$$ $$=\sqrt[]{16}=4$$

1 is both a Prime and a Composite Number $$True\ or\ False$$

$$False$$ 1 is neither a Prime nor a Composite Number

HCF of any two co-prime numbers is always 1 $$True\ or\ False$$

$$True$$ Example - HCF of 9 and 8 is 1, since they don't have any common factor other than 1

$$a=2^2\times3\times5$$ $$b=2\times3^2\times5^2\times7$$ $$LCM(a,b)=$$

$$2^2\times3^2\times5^2\times7$$ $$=6300$$

If 'p' is a prime number and p divides a 2 , then p divides 'a' also, where a is a positive integer. $$True\ or\ False$$

$$True$$ For example, if 3 divides 9 2 , then 3 will divide 9

$$12^n$$ , where n is a natural number, can have zero at the unit place. $$True\ or\ False$$

$$False$$ 12 n = (2 × 2 × 3) n As in the prime factors of 12, we don't have 5, therefore, it will never end with zero.

Three bells ring at intervals of 6, 12 and 18 minutes. If all three bells rang at 6 a.m., when will they ring together again? To solve this question, we have to find the LCM or the HCF .

$$LCM$$ To find when they will all ring together , we need a time that is a common multiple of 6, 12, and 18. The smallest such common time is the LCM .

144 cartons of Coke cans and 90 cartons of Pepsi cans are to be stacked in a canteen. If each stack is of the same height and is to contain a carton of the same drink. What would be the greatest number of cartons in each stack? This question is based on the concept of LCM or HCF

$$HCF$$ We want to divide both numbers (144 and 90) into equal groups. The number of cartons in each stack should be the same for Coke and Pepsi. To make the stacks as large as possible , we need the greatest common factor of 144 and 90.

$$3.14$$ is an irrational number $$True\ or\ False$$

$$False$$ 3.14 is a rational number as it can be written as $$\frac{314}{100}$$ It is an approximate value of $$\pi$$

The product of two consecutive positive integers is divisible by 2 $$True\ or\ False$$

$$True$$ In any pair of consecutive integers, there is always one even number and one odd number, so the entire product must be divisible by 2 .

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