Playing With Numbers(6th Grade > Mathematics ) Questions and answers for exam Preparation

6th Grade > Mathematics

PLAYING WITH NUMBERS MCQs

Total Questions : 100 | Page 1 of 10 pages

Question 1. What are prime numbers? Find the prime factorization of 2048. [3 MARKS]

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Definition: 1 Mark
Prime Factorisation: 2 Marks
All the numbers other than 1, whose only factors are 1 and the number itself are called prime numbers.
The prime factorizationof 2048 is shown below.

What Are Prime Numbers? Find The Prime Factorization Of 204...

∴

2048 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2

Question 2. Which of the following represents the prime factorisation of 60?

2 x 2 x 3 x 5
2 x 2 x 5
2 x 2 x 3
2 x 2 x 3 x 5 x 5

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Answer: Option A. -> 2 x 2 x 3 x 5
:
A
Prime factorisation is expressing a number as the product of its prime factors.
60 = 2 x 30
= 2 x 2 x 15
= 2 x 2 x 3 x 5
(2, 3 and5are prime numbers)
Hence, the prime factorisation of 60 is 2 x 2 x 3 x 5.

Question 3. What is the divisibility rule for 9? Is 621 divisible by 9? [2 MARKS]

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Rule: 1 Mark
Solution: 1 Mark
A number is said to be divisible by 9 if the sum of its digits is divisible by 9.
The given number is 621.
Now, 6+2+1=9, which is divisible by 9.

∴

621 is divisible by 9.

Question 4. 37 students are standing in a row. Every 4th student is wearing a cap. Every 5th student is wearing a coat. Which student in the row will be wearing both a cap and a coat? [3 MARKS]

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Steps: 2 Marks
Solution: 1 Mark
Every 4th student is wearing cap i.e. it is divisible by 4.
And every 5th is wearing a coat. i.e. it is divisible by 5.
So, if we want to find out which student is wearing both cap and coat, we need to find the LCM of 4 and 5.
LCM of 4,5 = 4

\times

5 = 20. Since they are co-prime numbers, their LCM will be the product of these numbers.
Hence, if a number is divisible by two co-prime numbers then it is divisible by their product also.

Question 5. Akashi was playing with the numbers. She found that a number is divisible by both 7 and 12.
Which is the least number of which both of these will be divisible? [3 MARKS]

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Steps: 2 Marks
Solution: 1 Mark
The lowest number which will be divisible by both of these numbers is the LCM of these numbers.
To find the LCM of the numbers first we will find out its prime factors
The factors of 7: 1, 7
The factors of 12: 1, 2, 3, 4, 6, 12
Since the only common factor is 1, the given two numbers are co-prime.
The LCM of these numbers is their product.

∴

The required number is 7

\times

12 = 84.

Question 6. State the divisibility rule for 4. Using divisibility test, determine which of the following numbers are divisible by 4?
(a) 4096 (b) 21084
[2 MARKS]

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Each option: 1 Mark
A number is divisible by 4 if the last two digits of the whole numberare divisible 4.
(a) Since number formed by tens and units digit is 96, which is divisible by 4. Hence, 4096 is divisible by 4.
(b) Since number formed by tens and units digit is 84, which is divisible by 4. Hence, 21084 is divisible by 4.

Question 7. Two numbers having _____ as the only common factor are called ________ numbers.

2, twin prime
2, co-prime
1, co-prime
1, twin prime

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Answer: Option C. -> 1, co-prime
:
C
Two numbers having 1 as the onlycommon factor are called co-prime numbers.
For example, 16 and 35 are co-prime number.
Factors of 16: 1, 2, 4, 8, 16
Factors of 35: 1, 5, 7, 35
Here, 1 is the only common factor.

Question 8. Every number is a multiple of ______________ .

5
2
itself
100

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Answer: Option C. -> itself
:
C
Every number is a multiple of itself.

Question 9. Which of the following numbers are divisible by 11 and 9 respectively?

10000001, 459756
9000001, 45975
4569874, 547952
4568947, 97455

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Answer: Option A. -> 10000001, 459756
:
A
To check the divisibilityof a number by 11, we find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is 0 or a number divisible by 11, then the number is divisible by 11.
For 10000001,
Sum of digits at odd places = 1
Sum of digits at even places = 1
difference = 1 - 1 = 0
Hence, 10000001 is divisible by 11
For divisibility by 9 - if the sum of the digits of a number is divisible by 9, then the number is divisible by 9.
The sum of digits of459756 is 36 which is divisible by 9.
Hence,459756 is divisible by 9.

Question 10. Composite numbers have more than _______ factors.

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Answer: Option D. -> 2
:
D
Composite numbers have more than 2 factors.
For example, factors of 4are 1, 2 and 4.