Factors and Multiples
the cube of the first no exceed their product by 2,the cube of the second no is smaller than their product by 3,and the cube of the third no exceeds their product by 3
A)3^(1/3) B)9^(1/3) C)2 D)any of these
How many four-digit numbers are there with less than 6 different prime factors?
- 1224 b. 8476 c. 9000 d. 7613
Find the highest power of 12 that will divide ( 536 - 1)is?
Find the solution:
536 - 1 = 2518 - 1 = (24 + 1)18 - 1 = 2418 + 18 x 2417 + ... + 18 x 24 + 1 - 1 = 122k.
536 - 1 = (4 + 1)36 - 1 = 122k.
So highest power of 12 that will divide the expression is 2
Q: 523abc is divisible by 7, 8 and 9. Then a x b x c is equal to?
Since 7,8 and 9 are co-prime, the number which is divisible by 7,8 and 9, must also be divisible by their L.C.M i.e. by 504.
Now let's have a look at the given number, 523abc. It should lie between 523000 and 523999.
The multiples of 504 lying in this range are 523152 and 523656. Two possible values of abc are 152 and 656.
a,b and c are distinct, so abc must be 152, hence a x b x c = 1 x 5 x 2 = 10
Find the smallest number with 20 divisors.
sir, please help
For how many integers x4 + x3 + x2 + x + 1 is a perfect square?
If the sum of two natural numbers is multiplied by each number separately, the products so obtained are 2418 and 3666. What is the difference between the numbers?
How many numbers less than 100 have exactly 7 composite factors?
How many natural numbers from 1 to 2011 has a sum of digits which is multiple of 5?
The sum of 20 numbers(may or may not be distinct)is 801. What is their minimum LCM?
(Data sufficiency question)
Is X divisible by 15?
I. X is a number formed by writing ten consecutive natural numbers side by side.
II. X is the number formed by multiplying the factorials of three consecutive natural numbers.
Sir, I think both the statements combined are sufficient to answer the question, since the number of digits in X is at least 10. So the three consecutive natural numbers taken must have been greater than 5? But the answer is that even together they are insufficient. Why so?
Find the total number of even factors of the L.C.M. of first 25 natural numbers.