RBSE Solutions Class 5 Maths Chapter 5 Multiples and Factors Exercise 5.2

Find the factors of 18, 32, 28, 42, 45, 56 through division.

Question 1. Find out the factors of given numbers.
(i) 7
(ii) 9
(iii) 16
(iv) 25
(v) 48
(vi) 63
Answer:
(i) The factors of 7 are 1 and 7.
(ii) The factors of 9 are 1, 3, and 9.
(iii) The factors of 16 are 1, 2, 4, 8, and 16.
(iv) The factors of 25 are 1, 5, and 25. Every number has at least two factors: 1 and itself.
(v) The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
(vi) The factors of 63 are 1, 3, 7, 9, 21, and 63.
In simple words: Factors are numbers that divide another number exactly, leaving no remainder. You find them by thinking of all the pairs of numbers that multiply to give the original number.

🎯 Exam Tip: To find all factors of a number, systematically check division by numbers starting from 1 up to the square root of the number. If a number divides it, its pair (the result of division) is also a factor.

Question 2. Find out the factors of given numbers,
(i) 8 and 12
(ii) 10 and 20
(iii) 7 and 16
(iv) 18 and 32
Answer:
(i) For 8 and 12:
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
The common factors of 8 and 12 are 1, 2, and 4.

(ii) For 10 and 20:
Factors of 10: 1, 2, 5, 10
Factors of 20: 1, 2, 4, 5, 10, 20
The common factors of 10 and 20 are 1, 2, 5, and 10. Common factors are numbers that are factors of two or more numbers.

(iii) For 7 and 16:
Factors of 7: 1, 7
Factors of 16: 1, 2, 4, 8, 16
The common factor of 7 and 16 is 1.

(iv) For 18 and 32:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 32: 1, 2, 4, 8, 16, 32
The common factors of 18 and 32 are 1 and 2.
In simple words: First, list all the numbers that can divide each given number without a remainder. Then, look for the numbers that appear in all the lists. Those are the common factors.

🎯 Exam Tip: When finding common factors, list all factors for each number first, then identify the numbers that appear in every list. This method helps avoid missing any common factors.

Question 3. Find out the highest common factors of 21 and 28.
Answer:
Factors of 21: 1, 3, 7, 21
Factors of 28: 1, 2, 4, 7, 14, 28
The highest common factor of 21 and 28 is 7. The highest common factor (HCF) is the largest number that divides two or more numbers without any remainder.
In simple words: List all the numbers that divide 21 and all the numbers that divide 28. Find the numbers that are in both lists. The biggest number in that common list is the highest common factor.

🎯 Exam Tip: Always list all factors for each number first to ensure you don't miss any, especially the highest one, when determining the HCF.

Question 4. Find out the highest number which can exactly divides 45 and 75.
Answer:
Factors of 45: 1, 3, 5, 9, 15, 45.
Factors of 75: 1, 3, 5, 15, 25, 75
Common factors of 45 and 75: 1, 3, 5, 15
The highest number that can exactly divide 45 and 75 is 15.
In simple words: We need to find the biggest number that divides both 45 and 75 perfectly. We list all the numbers that can divide 45, then all the numbers that can divide 75. The largest number that appears in both lists is the answer.

🎯 Exam Tip: This question asks for the Highest Common Factor (HCF). Listing all factors for both numbers and then identifying the largest common one is a reliable method.

Question 6. Find out the highest common factors of 15, 27 and 36.
Answer:
Factors of 15: 1, 3, 5, 15
Factors of 27: 1, 3, 9, 27
Factors of 36: 1, 2, 3, 4, 6, 12, 18, 36
Common factors of 15, 27, and 36: 1, 3
The highest common factor of 15, 27, and 36 is 3. The HCF is useful in simplifying fractions and understanding number relationships.
In simple words: First, find all the numbers that can divide 15, 27, and 36 separately. Then, look for the numbers that are present in all three lists. The largest of these numbers is the highest common factor.

🎯 Exam Tip: When finding the HCF for three numbers, ensure the common factors you identify are present in the factor list of all three numbers, not just two.

Question 7. Two milk containers filled with 20 litre and 30 litre of milk respectively. What will be the greatest(RBSEgners exactly?
Answer:
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The common factors of 20 and 30 are 1, 2, 5, 10.
The highest common factor is 10.
Therefore, the greatest measurement of a container that can measure the total milk of both containers exactly is 10 litres. This means a 10-litre container can be used to fill both without any milk left over.
In simple words: We need a container that can measure both 20 litres and 30 litres perfectly, without any milk left behind. We find the largest number that divides both 20 and 30. That number is 10, so a 10-litre container is the biggest one that can do the job.

🎯 Exam Tip: Problems asking for the "greatest measurement," "largest number," or "maximum capacity" often require finding the Highest Common Factor (HCF).