CBSE Class 6 Mathematics Playing With Numbers Worksheet Set 02

Question. Test the divisibility of The following numbers by 3.
i) 10038
ii) 20701
Answer : i) 10038
1+0+0+3+8=12,divisible by 3.
ii) 20701
2+0+7+0+1 =10,not divisible by 3.

Question. Test the divisibility of the following numbers by 9.
i) 2358
ii) 98712
Answer : i) 2358
Sum of digits=(2+3+5+8=18) so divisible by 9.
ii) 98712
Sum of digits= 9+8+7+1+2=27,so divisible by 9.

QuestionTest the divisibility of the numbers by 5.
i) 35208
ii) 723405
Answer : i) 35208
Unit place number is 8,so not divisible by 5.
ii) 723405
Unit place number is 5, so divisible by 5.

Question. Give an example of a number which is divisible by 2 but not by 4.
Answer : 2

Question. Test the divisibility of the following numbers by 4.
i) 63712
ii) 810624
Answer : i) 63712
Tens and unit place numbers Form 12,which is divisible by 4.
ii) 810624
Tens and unit place numbers Form24, which is divisible by 4.

Question. Test the divisibility of the following numbers by 2.
i) 2650
ii) 69435
iii) 367314
Answer : i) 2650
Unit place number is 0 ,so divisible by 2.
ii) 69435
Unit place number is 5, so not divisible by 2.
iii) 367314
Unit place number is 4 so divisible by 2.

Question. Test the divisibility of the following numbers by 7.
i) 6021
ii) 14126
Answer : i) 6021
(602-2 ×1=600) which is not divisible by 7.
ii) 14126
(1412-2×6=1400) this is divisible by 7.

Question. Test the divisibility of the following numbers by 6.
i) 46523
ii) 71232
Answer : i) 46523
46523 is divisible by 3but not divisible by 2,so not divisible by 6.
ii) 71232
71232 is divisible both by 2 and 3.so divisible by 6.

Solve the following crossword puzzle, hints are given below:

ACROSS

Question 2. Finding factors of a number.
Answer: DIVISION
In simple words: Division is the mathematical operation used to find the factors of a given number by checking which numbers divide it evenly without leaving a remainder.

Exam Tip: Remember that every division that results in a zero remainder gives us a factor and a quotient pair.

Question 10. Every number is a _________ of itself.
Answer: FACTOR
In simple words: Every non-zero number divides itself exactly, meaning every number is always a factor of itself.

Exam Tip: A number always has at least two standard factors: 1 and the number itself (except for the number 1).

Question 12. Smallest composite number.
Answer: FOUR
In simple words: The number 4 has more than two factors (1, 2, and 4), making it the smallest composite number.

Exam Tip: Numbers 2 and 3 are prime, so 4 is the first composite number in counting numbers.

Question 13. The smallest number of two digits which is a multiple of three.
Answer: TWELVE
In simple words: The first two-digit number is 10, and checking upwards, 12 is divisible by 3 (\(3 \times 4 = 12\)).

Exam Tip: Use the divisibility rule for 3: the sum of the digits must be a multiple of 3 (1 + 2 = 3).

Question 14. Largest number of one digit.
Answer: NINE

In simple words: Single-digit numbers range from 0 to 9, so 9 is the highest value among them.

Exam Tip: Adding 1 to the largest single-digit number gives the smallest two-digit number (9 + 1 = 10).

Question 15. If a number is divisible by two co-prime numbers, then it is _________ by their product also.
Answer: DIVISIBLE
In simple words: If a number is divisible by two numbers that share no common factors other than 1, it must also be divisible by their multiplication product.

Exam Tip: This is a fundamental property of numbers used extensively in testing divisibility by composite numbers like 12, 15, or 36.

DOWN

Question 1. A number which is the divisor of the given number.
Answer: FACTOR
In simple words: A factor is an exact divisor of a number that divides it completely without leaving any remainder.

Exam Tip: Factors are always less than or equal to the given number.

Question 3. Short name of highest common factor.
Answer: HCF
In simple words: HCF stands for Highest Common Factor, which is the greatest common divisor shared by two or more numbers.

Exam Tip: HCF is also commonly referred to as GCD (Greatest Common Divisor).

Question 4. The number of factors of a number.
Answer: FINITE
In simple words: Unlike multiples which are infinite, the total count of factors for any given number is always limited and countable.

Exam Tip: Remember that every number has a finite number of factors, whereas its multiples go on forever.

Question 5. Short form of lowest common multiple.
Answer: LCM
In simple words: LCM stands for Lowest Common Multiple, which is the smallest positive number that is a multiple of two or more numbers.

Exam Tip: LCM is frequently used to add or subtract fractions with different denominators.

Question 6. Two numbers having only 1 as a common factor.
Answer: COPRIME
In simple words: Two numbers are called co-prime (or relatively prime) if their only common positive factor is 1.

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

Question 7. A number having exactly two factors.
Answer: PRIME
In simple words: A prime number is divisible only by 1 and by itself, giving it exactly two distinct factors.

Exam Tip: 2 is the only even prime number; all other prime numbers are odd.

Question 8. Sum of an odd and an even number.
Answer: ODD
In simple words: Adding an odd number and an even number always results in an odd number (e.g., \(3 + 4 = 7\)).

Exam Tip: Memorize basic parity rules: Odd + Even = Odd, Odd + Odd = Even, Even + Even = Even.

Question 9. Sum of two odd numbers.
Answer: EVEN
In simple words: The sum of any two odd numbers is always an even number (e.g., \(3 + 5 = 8\)).

Exam Tip: Two equal parts can always be formed from an even sum, which is why it is divisible by 2.

Question 11. Factor of every number.
Answer: ONE
In simple words: The number 1 divides every integer completely, making it a universal factor for all numbers.

Exam Tip: 1 is neither prime nor composite because it has only one factor (itself).