Playing With Numbers - Free MCQ Test solutions, Class 6 1000+ Questions

• 1: Not a valid one’s digit for divisibility by 5.
• 2: Not a valid one’s digit for divisibility by 5.
• 3: Not a valid one’s digit for divisibility by 5.
• 4: Not a valid one’s digit for divisibility by 5.
• 5: Valid one’s digit for divisibility by 5.

• Co-prime numbers are numbers that have no common factors other than 1.
• If a number is divisible by two co-prime numbers, it means it can be evenly divided by both.
• When two numbers are co-prime, their least common multiple (LCM) is simply their product.
• Therefore, if a number is divisible by each of the two co-prime numbers, it must also be divisible by their product.

If a number is divisible by 10, then its one's digit must be 0. Therefore, the correct option is: 0

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

A natural number greater than 1 that is not prime is called a composite number. For example:

• 6 can be divided by numbers other than 1 and itself:
• 2
• 3

This makes 6 a composite number.

Every prime number is divisible only by itself. 1 and 2 is the smallest even number that is followed by condition that is so it as even prime number. 

These numbers have been taken and divisible by 2 so expect 2 all prime numbers are odd. There is no exception and number 2 is prime even number.

The smallest prime number that is even is 2. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

2 is the only even prime number because every other even number is divisible by 2, which means they have more divisors than just 1 and themselves, making them composite.

Therefore, the correct answer is A: 2.

Factors of a number are defined as numbers or algebraic expressions that divide a given number/expression evenly. We can also say, factors are the numbers which are multiplied to get the other number. For example, 1, 3 and 9 are the factors of 9, because 1 × 9 = 9 and 3 × 3 = 9.

So the number of factors of a given number are finite.

The number of multiples of a given number is infinite. Example : Multiples of 2 = {2,4,6,8,10,...} Multiples of 3 = { 3,6,9,12,15,18,...}

Sum of odd digits = 9 + 1 + 5 = 15

Sum of even digits = 0 + 1 + 3 = 4

Difference = 15-4 = 11
Difference is divisible by 11. Therefore, 901153 is divisible by 11.

A multiple of a number is always greater than or equal to the number itself. This is because multiples of a number are obtained by multiplying the number by positive integers (e.g., 2 × 3 = 6, 3 × 3 = 9, etc.). The first multiple of any number is the number itself, and subsequent multiples are greater than the number.

On the other hand:

• Factors of a number are divisors of the number and are always less than or equal to the number.
• Number does not fit in the context of the statement.

Therefore, the correct answer is C: multiple.

• To find the HCF (Highest Common Factor) of 18 and 48, we start by determining the prime factors of each number.
• Factors of 18: 2 x 3 x 3
• Factors of 48: 2 x 2 x 2 x 2 x 3
• Next, identify the common factors: both numbers share the factors 2 and 3.
• The HCF is found by multiplying the lowest powers of all common factors: 2 x 3 = 6.
• Thus, the HCF of 18 and 48 is 6.

Option 4: 3 and 4

Explanation: A number divisible by 12 must also be divisible by both 3 and 4 because:

• 12 is the product of 3 and 4 (i.e., 12=3×4).
• If a number is divisible by 12, it is also divisible by both of its factors, 3 and 4.

The exact divisors of a number are the numbers that divide it evenly (without leaving a remainder).

For the number 9, the divisors are:

• 1 (since every number is divisible by 1),
• 3 (since 9 ÷ 3 = 3),
• 9 (since 9 ÷ 9 = 1).

Out of the given options, 3 is the exact divisor of 9.

Thus, the correct answer is A: 3.

To determine the numbers by which a number divisible by 6 will also be divisible, consider the factors of 6:

- Factors of 6 are 2 and 3.
- Therefore, if a number is divisible by 6, it will also be divisible by 2 and 3.
- The correct answer is C: 2 and 3.

Factors of 27 = 3 x 3 x 3

Factors of 63 = 3 x 3 x 7

H.C.F. (27, 63) = 3 x 3 = 9

Answer: B
Solution:

• A factor of a number divides that number without leaving a remainder.
• The number 1 is a factor of every number because any number divided by 1 equals the number itself.
• For example, 7 ÷ 1 = 7 and 100 ÷ 1 = 100.
• Hence, 1 is the factor of every number.

The HCF of two consecutive numbers is always one. The reason behind this is that the two consecutive numbers do not have any common factor other than 1. Hence 1 becomes the highest common factor between two consecutive numbers.

The LCM of two coprime numbers is the product of the numbers.