Test: Prime Time - 1 - Class 6 MCQ

To solve this, we need to find the factors (divisors) of 48. The factors of 48 are:

1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

The largest factor of 48, which is the maximum number of trees that can be planted in one row, is 48 itself.

So, if the gardener plants 48 trees in one row, then there would be only one row of trees.

To find a number that is a multiple of both 7 and 2, we need to find the least common multiple (LCM) of 7 and 2.

• The multiples of 7 are: 7, 14, 21, 28, 35, 42, etc.
• The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, etc.

The smallest number that appears in both lists is 14.

So, the correct answer is: B: 14

A perfect square is a number that can be expressed as the square of an integer.

Let's check each option:

• A: 12 is not a perfect square because there is no integer that, when multiplied by itself, equals 12.
• B: 16 is a perfect square because 4 × 4 = 16
• C: 18 is not a perfect square because there is no integer that, when multiplied by itself, equals 18.
• D: 20 is not a perfect square because there is no integer that, when multiplied by itself, equals 20.

So, the correct answer is: B: 16

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

To determine the largest number of apples that can be in each group, we need to find the largest divisor of 56 that divides evenly.

The divisors of 56 are: 1, 2, 4, 7, 8, 14, 28, and 56.

The largest divisor of 56, excluding 56 itself, is 28.

The largest number of apples you can have in each group is 8 apples.

So, the correct answer is: D: 8 apples.

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

• The divisors of 18 are: 1, 2, 3, 6, 9, 18.
• The divisors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.

The greatest common divisor (GCD) is the largest number that appears in both lists. In this case, the GCD of 18 and 24 is 6.

Thus, the greatest number of marbles you can both split into equal groups is: C: 6 marbles.

To find the prime factorization of 56, we can divide it by the smallest prime numbers:

1. Start by dividing 56 by 2 (since 56 is even):
   56 ÷ 2 = 28
2. Now divide 28 by 2:
   28 ÷ 2 = 14
3. Divide 14 by 2:
   14 ÷ 2 = 7
4. Finally, 7 is a prime number, so we stop here.

The prime factorization of 56 is: 2 × 2 × 2 × 7

1. The divisors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
2. The largest divisor of 72 among the given options is 12.

Thus, the maximum number of candies that can be packed in each box is: D: 12 candies.

(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