Maharashtra Board Class 5 Maths Chapter 8 Multiples and Factors Set 33 Solutions

Std 5 Maths Chapter 8 Multiples And Factors

Question 1.(1) Write five three-digit numbers that are multiples of 2.
Answer:100, 102, 104, 106, 108.
In simple words: Numbers ending in 0, 2, 4, 6, or 8 are multiples of 2. These are also known as even numbers.

🎯 Exam Tip: To find multiples of a number, keep adding that number to the previous multiple. For three-digit numbers, start from 100 or the smallest three-digit multiple.

Question 1.(2) Write five three-digit numbers that are multiples of 5.
Answer:100, 105, 110, 115, 120.
In simple words: Any number that ends with a 0 or a 5 is a multiple of 5.

🎯 Exam Tip: Multiples of 5 are easy to identify by their last digit. Ensure the numbers selected are three-digit numbers.

Question 1.(3) Write five three-digit numbers that are multiples of 10.
Answer:100, 110, 120, 130, 140.
In simple words: Numbers that end in 0 are multiples of 10. They are also known as multiples of both 2 and 5.

🎯 Exam Tip: Multiples of 10 are always even and end in zero. This rule simplifies identification.

Question 2.Write 5 numbers that are multiples of 2 as well as of 3.
Answer:2 as well as of 3 means 2 and 3 that is multiples of 6. They are 6, 12, 18, 24, 30.
In simple words: A number that is a multiple of both 2 and 3 must also be a multiple of their least common multiple, which is 6.

🎯 Exam Tip: When a number is a multiple of two different numbers, it is also a multiple of their LCM (Least Common Multiple).

Question 3.A ribbon is 3 metres long. Can we cut it into 50 cm pieces and have nothing left over? Write the reason why or why not.
Answer:3 metres = 300 cm. We can cut it into 50 cm pieces. Since 300 is exactly divisible 50. That is 300 is multiples of 50. 300 ÷ 50 = 6 We will get 6 pieces, nothing is left over.
In simple words: Yes, the ribbon can be cut into 50 cm pieces with no leftover because the total length (300 cm) is an exact multiple of 50 cm.

🎯 Exam Tip: Always convert units to be consistent (e.g., metres to centimetres) before performing calculations involving lengths or quantities.

Question 4.A ribbon is 3 metres long. I need 8 pieces of ribbon each 40 cm long. How many centimetres shorter is the ribbon than the length I need?
Answer:1 piece of 40 cm, so for 8 pieces ribbon needed is 40 x 8 = 320 cm. But ribbon is 3 metre = 300 cm long. So ribbon is shorter by 320 - 300 = 20 cm.
In simple words: You need 320 cm of ribbon in total, but only have 300 cm, so the ribbon is 20 cm shorter than what is required.

🎯 Exam Tip: First, calculate the total length needed, then convert all measurements to the same unit, and finally, find the difference to determine how much shorter or longer an item is.

Question 5.If the number given in the table is divisible by the given divisor, put ✓ in the box. If it is not divisible by the divisor, put X in the box.
Answer:

Sr.No.	Number/Divisor	Divisor
		2	5	10
(1)	15	X	✓	X
(2)	30	✓	✓	✓
(3)	34	✓	X	X
(4)	46	✓	X	X
(5)	55	X	✓	X
(6)	63	X	X	X
(7)	70	✓	✓	✓
(8)	84	✓	X	X

In simple words: A number is divisible by 2 if it's even, by 5 if it ends in 0 or 5, and by 10 if it ends in 0. The table shows whether each number meets these conditions for the respective divisors.

🎯 Exam Tip: Practice divisibility rules for 2, 5, and 10: a number is divisible by 2 if its last digit is even; by 5 if its last digit is 0 or 5; and by 10 if its last digit is 0.

Prime And Composite Numbers

Some numbers are given in the tables below. Write all of their factors.

Numbers	Factors
2	1, 2
3	1, 3
4	1, 2, 4
5	1
6

Numbers	Factors
11
12
16
19
25

Dada : What do you notice on studying the table? Ajay : The number 1 is a factor of every number. Some numbers have only 1 and the number itself as factors. For example, the only factors of 3 are 1 and 3. Similarly, the factors of 2 are only 1 and 2 and the factors of 19 are only 1 and 19. Some numbers have more than two factors. Dada: Numbers like 2, 3, 19 which have only two factors are called prime numbers. A number which has only two factors, 1 and the number itself, is called a prime number. Ajay : What do we call numbers like 4, 6 and 16 which have more than two factors Dada: Numbers like 4, 6 and 16 are called composite numbers. A number which has more than two factors is called a composite number. Dada : Think carefully and tell me whether 1 is a prime or composite number. Ajay : The number 1 has only one factor, 1 itself, so I can't answer your question. Dada: You're right. 1 is considered neither a prime number nor a composite number. 1 is a number which is neither prime nor composite.

Multiples And Factors Problem Set 33 Additional Important Questions And Answers

Question 1.Write five three-digit numbers that are multiples of 3.
Answer:102, 105, 108, 111, 114.
In simple words: To find multiples of 3, you can start from a three-digit number and repeatedly add 3, ensuring the sum of the digits is always divisible by 3.

🎯 Exam Tip: Use the divisibility rule for 3: if the sum of a number's digits is divisible by 3, then the number itself is divisible by 3. Ensure the numbers are within the three-digit range.

Question 2.Write five two-digit numbers that are multiples of 7.
Answer:14, 21, 28, 35, 42
In simple words: Multiples of 7 are found by multiplying 7 by an integer. These numbers are obtained by skipping 6 numbers and landing on the seventh when counting.

🎯 Exam Tip: Listing multiples by repeated addition or multiplication (7 x 2, 7 x 3, etc.) is a reliable method to find them for any given number.

Question 3.Write five three-digit numbers that are multiples of 4.
Answer:112, 116, 120, 124, 128.
In simple words: A number is a multiple of 4 if the number formed by its last two digits is a multiple of 4.

🎯 Exam Tip: Apply the divisibility rule for 4: check if the number formed by the tens and units digit is divisible by 4. This simplifies finding multiples of 4 for larger numbers.

Question 4.Write 5 numbers that are multiples of 3 as well as 5.
Answer:3 as well as 5 means 3 and 5. i.e. multiples of 15. They are 15, 30, 45, 60, 75.
In simple words: Numbers that are multiples of both 3 and 5 are exactly the multiples of their least common multiple, which is 15.

🎯 Exam Tip: When a number must be a multiple of two different numbers, find their LCM; then, the required numbers are multiples of this LCM.

Question 5.A string is 4 metres long. Can we cut it into 50 cm pieces and have nothing left over?
Answer:4 metres = 400 cm. We can cut it into 50 cm pieces. Since 400 is exactly divisible by 50. That is 400 is multiple of 50 400 ÷ 50 = 8 We will get 8 pieces. Nothing is left over.
In simple words: Yes, a 4-metre string (400 cm) can be cut into 8 pieces of 50 cm each, with no remainder, because 400 is perfectly divisible by 50.

🎯 Exam Tip: Convert all measurements to a common unit (e.g., centimetres) before performing division or multiplication to ensure accuracy in your calculations.

Question 6.A paper Is 2 metres long. I need 8 pieces of paper each 30 cm long. How many centimetres shorter is the paper than the length I need?
Answer:A piece of 30 cm, so for 8 pieces paper needed is 30 x 8 = 240 cm. But paper is 2 metre = 2 x 100 = 200 cm long. So paper is shorter by 240 - 200 = 40 cm
In simple words: You need a total of 240 cm of paper, but you only have 200 cm. Therefore, the paper is 40 cm shorter than the required length.

🎯 Exam Tip: Remember to convert metres to centimetres (1 metre = 100 centimetres) for consistent calculations, especially when comparing different units of length.

Question 7.If the number given in the table is divisible by the given divisor, put P in the box. If it is not divisible by the divisor, put X in the box.
Answer:

Number/Divisor	Divisor
	2	5	10
85	X	✓	X
90	✓	✓	✓
92	✓	X	X
95	X	✓	X
97	X	X	X
100	✓	✓	✓

In simple words: A number is divisible by 2 if it's even, by 5 if it ends in 0 or 5, and by 10 if it ends in 0. 'P' indicates divisibility, and 'X' indicates not divisible based on these rules.

🎯 Exam Tip: Understand and apply the basic divisibility rules for 2, 5, and 10 to correctly mark 'P' or 'X' in the table. 'P' is used instead of '✓' as per question instruction.