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Which of the following numbers is divisible by 9?
Consider 90, 76,185
We know that the sum of the digits = 9 + 0 + 7 + 6 + 1 + 8 + 5 = 36
Thus, 36 is divisible by 9 thus 9076185 is divisible by 9.
Which of the following numbers is divisible by 11?
Consider 2,22,22,222,
We know that the difference of the sum of alternate digits 2 + 2 + 2 + 2 = 8 and 2 + 2 + 2 +2 = 8 is 0.
Therefore, the number is divisible by 11.
If 1688*2 is divisible by 3, then * can take the value of?
Sum of the given digits =
We know that which is a multiple of 3
Hence required digit is 2.
*95 is a threedigit number with * as a missing digit. If the number is divisible by 6, the missing digit is?
Sum of the given digits
Multiple of 3 greater than 14 is 15.
So, we get
Hence, the required digit is 1.
What least value should be given to * so that the number 4971*4 is divisible by 9?
We know that the sum of the given digits
Multiple of 9 greater than 25 is 27
Difference between them
Therefore, the smallest required digit is 2.
What least number be assigned to * so that number 356*47 is divisible by 11?
We know that the sum of the digits at odd places
In the same way the sum of the digits at even places
Difference between them =
So, the required number is 1.
What least number be assigned to * so that the number 63576*2 is divisible by 8?
We know that a number is divisible by 8 if the number formed by its last three digits is divisible by 8.
Hence, 63, 57, 6*2 is divisible by 8 if 6*2 is divisible by 8.
Therefore, the least value of * will be 3.
Which one of the following numbers is exactly divisible by 11?
We know that the sum of digits at odd places
The same way the sum of digits at even places
So, the difference between them
Hence, 4, 15,624 is divisible by 11.
The sum of the prime numbers between 60 and 75 is
We know that the prime numbers between 60 and 70 are 61 and 67.
So, their sum is
If 1*56 is divisible by 3, which of the following digits can replace *?
We know that the sum of the given digits
12 is a multiple of 3 then the required digit is 0.
____ is the HCF of two consecutive natural numbers.
We know that the HCF of any two consecutive natural numbers is 1 as two consecutive natural numbers are always coprime.
______ is the HCF of two consecutive even numbers.
The HCF of two consecutive even numbers is always 2.
______ is the HCF of two consecutive odd numbers.
HCF of two consecutive odd numbers is 1.
_____ is the HCF of an even number and an odd number.
Some of the examples are:
HCF of 6 and 9 is 3.
HCF of 8 and 21 is 1.
HCF of 9 and 36 is 9.
There is no fixed number which can be HCF and LCM.
The LCM of 12, 26 and 4 is
Prime Factorization of 4 is:
Prime Factorization of 12 is:
Prime Factorization of 26 is:
LCM =
If the HCF of two number is 14 and their product is 490, then their LCM is
Product of HCF and LCM = Product of two numbers
By substituting the values
14 × LCM = 490
LCM =
The least number divisible by 4,9,12,22 and 26 is
Prime Factorization of 4 is:
Prime Factorization of 9 is:
Prime Factorization of 12 is:
Prime Factorization of 22 is:
Prime Factorization of 26 is:
LCM
The smallest number which when diminished by 3 is divisible by 4,9,12,22 and 26 is
Prime Factorization of 4 is:
Prime Factorization of 9 is:
Prime Factorization of 12 is:
Prime Factorization of 22 is:
Prime Factorization of 26 is:
LCM
So, the required smallest number = LCM of (11, 28, 36, 45) + 3
We get the required smallest number = 5148 + 3 = 5151
Three numbers are in the ratio 5:2:3 and their HCF is 6, the numbers are
We know that the three numbers are 5× HCF, 2 × HCF, and 3 × HCF,
i.e., , and
Hence, the numbers are 30, 12 and 18.
The ratio of two numbers is 6:2 and their HCF is 4. Their LCM is
We know that the two numbers are 6 × HCF and 2 × HCF
It can be written as
6 × 4 = 24 and 2 × 4 = 8
So, we get
LCM of 24 and 8 = 24