Test:Factors & Mulitples - 3 - CTET & State TET MCQ

• The HCF of two coprime numbers is always 1.
• For example, 5 and 9 are coprime numbers, there, HCF (5, 9) = 1.

No, it is not a prime number.

The product of 2 co-prime numbers is equal to their LCM.

Hence, if one number is 16 other one is 

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Hence, 3 is a factor of 36.

In number theory, Co-prime numbers are those numbers if the only positive factor that divides them is 1.

Here,

Option A: (16,18) Factors that divide both of them are 1,2.

Option B: (11,48) Factor that divides both of them is 1.

Option C: (8,23) Factor that divides both of them is 1.

In reference to above definition both b and c are co-prime numbers.

LCM is divisible by HCF.

Hence, 8 cannot be the HCF  because 84 is not divisible by 8.

Let the other number be x

Product of two numbers = HCF × LCM 

 x × 36 = 6 × 144

 Hence, the other number is x = 24

The Prime numbers between the numbers 1 to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Here, we can see that the total count of prime numbers is 25.

Using divisibility rule:

9+1+8+5+7+3 = 33,

33 is divisible by 3 ( 11×3)

So, 918573 is divisible by 3.

A factor of a number is always less than or equal to the given number. Every number except 0 and 1 has at least two factors, 1 and itself.

A factor of a number is always less than or equal to the given number. Every number except 0 and 1 has at least two factors, 1 and itself.

Product of numbers = LCM x HCF

Let the other number be y

6 x 432 = 48 x y

y = 54

Hence, the other number is 54.

• Composite numbers are numbers with more than two factors. 
• 4, 6, 8, 9, 10, 12 have more than two factors, hence they are composite numbers.

• Odd numbers are whole numbers that cannot be divided exactly into pairs.
• 3, 7, 9, 11, 13 cannot be divided into pairs, hence they are odd numbers.

H.C.F of two numbers is the highest factor present in both the numbers.

So we can say, if the HCF of two numbers is 9 then the two numbers can be 9x and 9y where x and y are co-prime.

The LCM of these two numbers = product of these two numbers.

So, LCM of 9x and 9y = 9xy (Only one 9 in the LCM because it is a common factor of both the numbers).

Hence, we can conclude that the LCM must be an integral multiple of 9 as x and y are integers.                   

From the options given only 48 is the number which is not an integral multiple of 9. So it can never be the LCM.

The sum of the digits is calculated as follows:
3 + 6 + 3 + 0 = 12
12 is not divisible by 9. Therefore, 3630 is not divisible by 9.

The value of LCM(3, 4, 5) will be the smallest number that is exactly divisible by 3, 4, and 5.
Multiples of 3, 4, and 5:

• Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 48, 51, 54, 57, 60, . . . .
• Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 52, 56, 60, . . . .
• Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 45, 50, 55, 60, . . . .

Therefore, the LCM of 3, 4, and 5 is 60.

The last digits of any number must end with 0 or 5 to be divisible by 5.
The last digit of 5695 is 5.
Therefore, 5695 is divisible by 5.

190 = 2 x 5 x 19

152 = 2 x 2 x 2 x 19

171 = 3 x 3 x 19

The common factor of the numbers is 19. 

Hence, the HCF of 190 , 152 , 171 is 19.

Sum of digits is 1+2+3+4+5 = 15 , which is divisible by 3 .
So the number 12345 is divisible by 3