The correct option is **B**

(Video) How to find smallest Number having 12 factors in 30 seconds24

(Video) How to find smallest number having 27 factorsNumber of the form paqbrc (where p, q and r are primes) has (a + 1) (b + 1) (c + 1) factors.

So, if some number has 8 factors (a + 1)(b + 1)(c + 1) should be 8.

8 can be written as 8 or 4×2 or 2×2×2.

If a number has to have 8 factors, it should be in one of the following forms,

p7⟹7+1=8 factors

p3q1⟹4×2=8 factors

pqr⟹2×2×2=8 factors

Let us deduce the smallest possible number in each form.

p7⟹27

p3q1⟹23×3=24

pqr⟹2×3×5=30

(Video) Multiples vs. Factors | What are Multiples and Factors? | Math with Mr. J Therefore, smallest number that has exactly 8 factors = 24.

(Video) How to find smallest Number having 10 and 15 factors in 30 seconds(Video) What is the smallest positive integer that has 6, 8, and 10 as factors?

The correct option is **B**

24

Number of the form paqbrc (where p, q and r are primes) has (a + 1) (b + 1) (c + 1) factors.

So, if some number has 8 factors (a + 1)(b + 1)(c + 1) should be 8.

8 can be written as 8 or 4×2 or 2×2×2.

If a number has to have 8 factors, it should be in one of the following forms,

p7⟹7+1=8 factors

p3q1⟹4×2=8 factors

pqr⟹2×2×2=8 factors

Let us deduce the smallest possible number in each form.

p7⟹27

p3q1⟹23×3=24

pqr⟹2×3×5=30

Therefore, smallest number that has exactly 8 factors = 24.

## FAQs

### What are all the numbers with 8 factors? ›

**24, 30, 40, 42, 54, 56, 66, 70, 78 and 88** .

**What is the smallest number with 8 divisors? ›**

The smallest number with 8 divisors would be 30 = 2*3*5 if the theorem always held, but in fact the smallest number with 8 divisors is **24**.

**What is the smallest number with 7 factors exactly? ›**

So, any number that has 7 factors will have p = 0 and q = 6. i.e., the number will have only one prime factor. 2 is the smallest prime number. So, the smallest number that will have 7 factors, **N = 2 ^{6} = 64**.

**What is the smallest number of a factor? ›**

Hence, **1** is the smallest factor of all numbers.

**Does the number 24 have 8 factors? ›**

**There are a total of eight factors of 24**, they are 1, 2, 3, 4, 6, 8, 12 and 24. Pair factors of 24 are the numbers, which gives the result as 24 when multiplied together in pairs. Its pair factors are (1, 24), (2, 12), (3, 8), and (4, 6).

**Is 8 a factor of every number? ›**

Therefore, **1 is a factor of every number** and every number is a factor of itself.

**Which number is exactly divisible by 8? ›**

**If the last three digits of a number are divisible by 8, then the number is completely divisible by 8**. Example: Take number 24344. Consider the last two digits i.e. 344. As 344 is divisible by 8, the original number 24344 is also divisible by 8.

**What is the smallest multiple of 8? ›**

The multiples of 8 are **8, 16, 24, 32, 40, 48, 56, 64, 72, 80**… and so on.

**Which number are exactly divided by 8? ›**

A number is divisible by 8 **if its last three digits are divisible by 8**. For example, 880 and 905,256 are divisible by 8 but 74,513 is not divisible by 8. To check divisibility by 8, divide the last three digits of the number by 8. If the result is a whole number, then the original number is divisible by 8.

**What is the smallest number with exactly 10 factors? ›**

Hence the correct option is **48**.

### What is the smallest number with exactly 9 factors? ›

So if a number has 9 distinct factors, then it is either in the form or . The smallest number is **256**, with factors 1, 2, 4, 8, 16, 32, 64, 128, 256. The smallest is 36 with factors 1, 2, 3, 4, 6, 9, 12, 18, 36.

**What is the smallest number with exactly 5 factors? ›**

Hence, **16** is the number with exactly 5 factors.

**What is the smallest number that has 4 factors? ›**

Answer: 210 is the smallest number having four different prime factors.

**What is the smallest number with exactly 3 factors? ›**

The number 4 is the smallest positive integer that has exactly three factors: **1,2 and 4**.

**What is the smallest number with only 6 factors? ›**

For example, for n=6, f(6)=**24**, because 24 has the 6 distinct factors {2,3,4,6,8,12}, and 24 is the smallest integer with 6 factors.

**Is 8 a factor of 44? ›**

The factors of 44 are **1, 2, 4, 11, 22 and 44**.

**Do 8 and 35 have common factors? ›**

When you compare the two lists of factors, you can see that **the only common factor is 1**. So, in this case, the GCF of 35 and 8 is 1.

**How many factors does 38 have? ›**

Answer: There are **four** factors of 38. They are 1, 2, 19 and 38.

**Is 0 a factor of 8? ›**

**Zero is not the factor of any number** because if we divide a number by zero, the value is not defined.

**Is 8 a factor of 32 yes or no? ›**

Factors of 32 = 1, 2, 4, 8, 16, 32.

### What numbers are not a factor of 8? ›

Factors of 8 are 1, 2, 4, and 8. When we divide 8 by 3, 5, 6, and 7, it leaves a reminder. Thus, these numbers are not the factors of 8 which means **3, 5, 6, and 7** are not the factors of 8.

**Is 2564 divisible by 8? ›**

So, 2564 is **not divisible by 8**.

**Is 654 divisible by 8? ›**

The last three-digit of 98654 is 654 and 654 is **not divisible by 8**.

**Is 0 divisible by 8? ›**

Note: **Zero is divisible by any number (except by itself)**, so gets a "yes" to all these tests.

**Is 8 a factor of 40? ›**

Factors of 40: **1, 2, 4, 5, 8, 10, 20 and 40**.

**What is the smallest 8 digit numeral? ›**

The smallest 8 digit number is **1 , 00 , 00 , 000** .

**Which is the smallest number with exactly two factors? ›**

Hence, a number which has only two factors is called a **prime number** .

**Is 624 divisible by 8? ›**

So,Is 624 divisible by 8? **Yes**.

**Is 36 divisible by 8? ›**

The hundreds digit in 36 is 0, which is even, and the last two digits are 36. Thus, we use the Even Rule above: **36 is not divisible by 8**, therefore 36 is not divisible by 8.

**Is 6132 divisible by 8? ›**

∴ the given number 6132 is **not divisible by 8**.

### What number has 8 factors and is less than 100? ›

So Number 40 contains exactly 8 divisors (I have taken divisors as factors ).

**What prime number has 8 factors? ›**

...

Sum of Factors of 8: 15.

1. | What are Factors of 8? |
---|---|

3. | Factors of 8 By Division Method |

4. | Factors of 8 By Prime Factorization |

5. | Thinking Out of The Box! |

6. | Factors of 8 in Pairs |

**What are the multiples of 8 up to 100? ›**

What are the multiples of 8 through 100? The multiples of 8 until 100 are **8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96**.

**What are a list of multiples of 8? ›**

The first few multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 and 96.

**Which number is 8 not a factor of? ›**

Factors of 8 are 1, 2, 4, and 8. When we divide 8 by 3, 5, 6, and 7, it leaves a reminder. Thus, these numbers are not the factors of 8 which means 3, 5, 6, and 7 are not the factors of 8.

**Is 8 a factor of 70 yes or no? ›**

Factors of 70 are: 1, 2, 5,7,14, 10, 35 and 70 = 8 factors.

**Is 16 a factor of 8? ›**

As the number 16 is a composite number, it has more than one factor. **The factors of 16 are 1, 2, 4, 8 and 16**. Similarly, the negative factors of 16 are -1, -2, -4, -8 and -16.

**Is 8 a factor of 40 true or false? ›**

There are 8 factors of 40, which are 1, 2, 4, 5, 8, 10, 20 and 40.

**Is 48 a multiple of 8 yes or no? ›**

he first eight multiples of 8 are 8, 16, 24, 32, 40, 48, 56, and 64.

**Is 8 a factor of 100? ›**

Hence **8 is not a factor of 100**. As 3 is a factor of 9 and 3 is not a factor of 100, 9 is also not a factor of 100.

### Is 48 a factor of 8? ›

Factors of 48 by Division Method

Thus, **the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48**.

**What is the least common multiple of 8? ›**

Multiples of 8 are: 8, 16, 24, 32, 40, .... So **24** is the least common multiple (we can't find a smaller one!)

**What number is not exactly divisible by 8? ›**

A number is divisible by 8 if its last three digits are divisible by 8. For example, 880 and 905,256 are divisible by 8 but **74,513** is not divisible by 8. To check divisibility by 8, divide the last three digits of the number by 8. If the result is a whole number, then the original number is divisible by 8.