Test: Prime Time - 1 - Class 6 MCQ

A number is a multiple of 4 if it can be divided by 4 with no remainder.

Let's check each option:

• A: 14 ÷ 4 = 3.5 (not a multiple of 4)
• B: 18 ÷ 4 = 4.5 (not a multiple of 4)
• C: 20 ÷ 4 = 5 (a multiple of 4)
• D: 22 ÷ 4 = 5.5 (not a multiple of 4)

So, the correct answer is: C: 20

The prime factorization of 56 involves breaking it down into its basic components, which are prime numbers. Here’s how it works:

• Start with 56, which is composite.
• It can be expressed as 4 × 14.
• Next, break down 4 into 2 × 2.
• Also, break down 14 into 2 × 7.
• Now, combine these: 56 = 2 × 2 × 2 × 7.

All the factors here, 2 and 7, are prime numbers. Therefore, the prime factors of 56 are:

• 2 (appears three times)
• 7 (appears once)

Every number greater than 1 has a unique prime factorization. The process involves continually breaking down composite numbers until only primes remain. For example, the prime factorization of a prime number like 7 is simply 7, as it cannot be divided further.

In summary, the prime factorization of 56 is: 2 × 2 × 2 × 7

Factors of 14: 1, 2, 7, 14

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Now, let's check which number appears in both lists:

• A: 2 is a factor of both 14 and 36.
• B: 3 is not a factor of 14.
• C: 7 is a factor of 14 but not 36.
• D: 12 is a factor of 36 but not 14.

So, the correct answer is: A: 2

A number is divisible by 8 if the last three digits form a number that is divisible by 8. For example:

• The number 112 is checked: 112 ÷ 8 = 14.
• Since there is no remainder, 112 is divisible by 8.

Thus, 112 is the correct answer.

The prime numbers between 21 and 30 are: 23, 29

Thus, there are a total of 2 prime numbers in this range.

Co-prime numbers are defined as pairs of numbers that have no common factor other than 1. In the case of 4 and 9:

• They do not share any factors besides 1.
• Thus, they are classified as co-prime.

For example:

• 15 and 39 are not co-prime because they share a common factor of 3.
• However, 4 and 9 are co-prime.

To find the prime factorization of 60, we can break it down into its smallest prime factors:

• 1. 60 is divisible by 2 (the smallest prime number): 60 ÷ 2 = 30
• 2. 30 is also divisible by 2: 30 ÷ 2 = 15
• 3. 15 is divisible by 3: 15 ÷ 3 = 5
• 4. 5 is already a prime number.

Thus, the prime factorization of 60 is 2 × 2 × 3 × 5.

A prime number has only two factors: 1 and itself. The number 23 is only divisible by 1 and 23, confirming it as a prime number.

(a) 20: Prime factorization: 20 = 2 × 2 × 5
It has only 2 distinct primes (2 and 5).

(b) 165: Prime factorization: 165 = 3 × 5 × 11
It has exactly 3 distinct primes (3, 5, and 11).

(c) 45: Prime factorization: 45 = 3 × 3 × 5
It has only 2 distinct primes (3 and 5).

(d) 147: Prime factorization: 147 = 3 × 7 × 7
It has only 2 distinct primes (3 and 7).

The number that is the product of exactly three distinct prime numbers is: (b) 165

A factor is a number that divides another number exactly, leaving no remainder. The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

All of these numbers can divide 24 without any remainder, confirming they are its factors.