Number of Factors of a Numbers

Q.

Which are the numbers between 1 and 100 that have exactly three factors?

1. 1, 4, 9, 25, 36, 49, 16, 64, 81, 100

2. 4, 9, 25, 49.

3. 9, 25, 49, 100

4. 49, 16, 64, 81, 100

Q.

What is the smallest number with exactly five factors?

1. 32

2. 36

3. 16

4. 20

Q. Find the cube root of 42875.

1. 25
2. 35
3. 45
4. 55

Q.

How many even factors does the number 720 have in all?

1. 20

2. 24

3. 10

4. 30

Q.

How many factors does a product of three distinct primes have?

1. 6

2. 8

3. 3

4. 2

Q.

If $X$ and $Y$ are the sets of all positive divisors of $400$ and $1000$, respectively (including $1$ and the number). Then, $n(XintersectionY)$ is equal to:

1. $4$

2. $6$

3. $8$

4. $10$

5. $12$

Q. Which of these numbers is a product of three distinct primes?

1. 18
2. 12
3. 27
4. 30

Q.

How many factors does 2000 have ?

1. 10

2. 15

3. 20

4. 25

Q.

If $p$ is a prime number, how many factors does $p\times p$ have?

1. 1

2. 2

3. 3

4. $p$

Q.

Any number with exactly four factors is a product of two distinct primes.

1. True

2. False

Q. Classify the following numbers as having odd or even number of factors: (i) 36 (ii) 48 (iii) 65 (iv) 81

Q.

What is the square root of $145$?

Q.

Which of the following have odd number of factors?

1. 64

2. 81

3. 50

4. 52

Q.

Question 12 (b)

Fill in the blanks:

A number which has more than two factors is called a ________.

Q.

Choose the set of all numbers between 1 and 70 which have odd number of factors?

1. 5, 10, 16, 30, 36, 55, 78, 95

2. 1, 4, 9, 25, 36, 16, 49, 64

3. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 53, 57, 61, 67

4. 1, 4, 9, 25, 36, 16, 49, 64, 81, 100

Q. How many factors does a product of four distinct primes have?

1. 5
2. 10
3. 4
4. 16

Q. Find the number of factors of 8.

1. 2
2. 3
3. 4
4. 5

Q.

Which of the following methods is/are useful in finding the square root of a number?

1. Exponent method

2. Prime factorization method

3. Long division method

4. Both prime factorization and long division method

Q.

Which of the following have exactly three factors?

1. 13

2. 25

3. 125

4. 21

Q. The number of factors of 24 is .

1. 6
2. 4
3. 8

Q. The number of factors of 396 is .

1. 12
2. 8
3. 7

Q. Find the square root of:

(3) 3025

Q. In $aN=\{ax:x\in N\}$ and $bn\cap cN=dN$, where $b,c\in N$ are relatively prime, then

1. $d=bc$
2. $b=cd$
3. $c=bd$
4. $Noneofthese$

Q. How many factors does a product of three distinct primes have? What about a product of $4$ distinct primes?
[4 marks]
[SCERT, Kerala]
[Number of Factors]

Q.

Choose the number that has exactly 3 factors.

1. 16

2. 27

3. 25

4. 8

Q. Classify the following numbers as having odd or even number of factors: (i) 36 (ii) 48 (iii) 65 (iv) 81

Q. Find the square root of:

(5) 10404

Q.

Find the number of steps required to reduce 169 to 0 by the method of repeated subtraction.

1. 9

2. 15

3. 11

4. 13

Q.

Which of the following have exactly four factors?

1. 15

2. 27

3. 8

4. 16

Q. Complete the pattern:
4, 9, 25, ______

Kindly explain