CBSE Class 6 Mathematics Playing with Numbers Assignments Set 03

VI - Mathematics Assignment No - 08 - Playing With Numbers

Fill the gaps in the following statements:

Question 1. A factor of a number is an exact ________ of that number.
Answer: divisor
In simple words: A factor divides a number completely without leaving any remainder, making it an exact divisor.

Exam Tip: Remember the basic definition that factors are exact divisors of a given number.

Question 2. Every number is a ________ of itself.
Answer: multiple
In simple words: Multiplying a number by 1 gives the number itself, so every number is a multiple of itself.

Exam Tip: Keep in mind that a number multiplied by 1 equals itself.

Question 3. Every multiple of a given number is ________ than or ________ to that number.
Answer: greater, equal
In simple words: Multiples are obtained by multiplying by 1, 2, 3, etc., so they are either greater than or equal to the original number.

Exam Tip: Unlike factors which are smaller or equal, multiples are always greater than or equal to the number.

Question 4. Every number is a ________ of each of its factors.
Answer: multiple
In simple words: If 3 is a factor of 12, then 12 is a multiple of 3.

Exam Tip: Factors and multiples are inverse concepts regarding divisibility.

Question 5. Every factor of a number is less than or ________ to the given number.
Answer: equal
In simple words: The factors of a number can never be larger than the number itself; the largest factor is the number itself.

Exam Tip: Factors are finite and bounded by the number itself.

Question 6. Every number is a ________ of itself.
Answer: factor
In simple words: Every non-zero number divides itself exactly, so it is a factor of itself.

Question 7. ________ is a factor of every number.
Answer: One
In simple words: 1 divides every whole number without a remainder.

Exam Tip: 1 is a universal factor.

Question 8. ________ is the only ________ prime number.
Answer: Two, even
In simple words: 2 is the only even number that has only two factors (1 and itself). All other even numbers are divisible by 2.

Exam Tip: Memorize this exception: all other prime numbers are odd.

Question 9. The H.C.F. of two or more nos. is the ________ of their common factors.
Answer: highest
In simple words: HCF stands Highest Common Factor, which is the greatest factor common to all the given numbers.

Exam Tip: HCF = Highest Common Factor.

Question 10. The L.C.M. of two or more nos. is the ________ of their common multiples.
Answer: lowest
In simple words: LCM stands for Lowest Common Multiple, which is the smallest multiple shared by the numbers.

Exam Tip: LCM = Lowest Common Multiple.

Question 11. Two nos. with only 1 as a common factor are called ________ nos.
Answer: co-prime
In simple words: Numbers that share no common factors other than 1 are known as co-prime or relative prime numbers.

Exam Tip: Co-prime numbers do not need to be prime numbers individually (e.g., 8 and 9).

Question 12. If a no. is divisible by another no. then it is divisible by each of the ________ of that number.
Answer: factors
In simple words: If a number is divisible by 12, it is also divisible by all the factors of 12 (like 1, 2, 3, 4, 6).

Exam Tip: Use this rule to test divisibility by composite numbers.

Question 13. Divisibility by 2, 5, 10 can be seen by just the ________.
Answer: Last digit
In simple words: You only need to look at the units place digit to check divisibility by 2, 5, and 10.

Exam Tip: Check the last digit: even for 2, 0 or 5 for 5, and 0 for 10.

Question 14. Divisibility by 3, 9 is checked by finding the ________ of ________ digits.
Answer: Sum, all
In simple words: Add up all the digits of the number; if that sum is divisible by 3 or 9, the number itself is divisible.

Exam Tip: Sum of digits rule applies to both 3 and 9.

Question 15. Divisibility by 11 is checked by comparing the ________ of digits at ________ and ________ places.
Answer: sum, odd, even
In simple words: Find the difference between the sum of digits at odd places and even places from the right. If the difference is 0 or a multiple of 11, the number is divisible by 11.

Exam Tip: Always count digit positions from right to left starting from 1.