Maharashtra Board Solutions Class 5-Maths (Problem Set 33) - Part 2: Chapter 8- Multiples and Factors
Maharashtra Board Solutions Class 5-Maths (Problem Set 33) - Part 2: Chapter 8- Multiples and Factors

Class 5: Maths Chapter 8 solutions. Complete Class 5 Maths Chapter 8 Notes.

Maharashtra Board Solutions Class 5-Maths (Problem Set 32) – Part 2: Chapter 8- Multiples and Factors

Maharashtra Board 5th Maths Chapter 8, Class 5 Maths Chapter 8 solutions

Important Questions and Answers.

Write the factors of the following numbers.

(1) 8
Answer:
8 is exactly divisible by 1, 2, 4, 8.
So, 1, 2, 4, 8 are factors of 8.

(2) 5
Answer:
5 is exactly divisible by 1, 5.
So, 1, 5 are factors of 5.

(3) 14
Answer:
14 is exactly divisible by 1, 2, 7, 14.
So, 1, 2, 7, 14 are the factors 14.

(4) 10
Answer:
10 is exactly divisible by 1, 2, 5, 10.
So, 1, 2, 5, 10 are the factors of 10.

(5) 7
Answer:
7 is exactly divisible by 1, 7.
So, 1, 7 are factors of 7.

(6) 22
Answer:
22 is exactly divisible by 1, 2, 11, 22.
So, 1, 2, 11, 22 are the factors of 22.

(7) 25
Answer:
25 is exactly divisible by 1, 5, 25.
So, 1, 5, 25 are the factors of 25.

(8) 32
Answer:
32 is exactly divisible by 1, 2, 4, 8,16, 32.
So, 1, 2, 4, 8, 16, 32 are the factors of 32.

(9) 33
Answer:
33 is exactly divisible by 1, 3, 11, 33.
So, 1, 3, 11, 33 are the factors of 33.

Multiples

Dada : You know what a divisor and a dividend is. Do you know what a multiple is?

Anju : I don’t know what a multiple is, but I think it must be related to multiplication.

Dada : Right ! Let me give you an example. You can solve 20 ÷ 5, can’t you?

Anju : Yes. When we divide the dividend 20 by the divisor 5, the quotient is 4 and the remainder is 0.

Dada : When the division of a dividend leaves no remainder, the dividend is said to be a multiple of the divisor. In such a case, the dividend is the product of the divisor and the quotient. Here, 20 is a multiple of 5, but 21 is not.

Now tell me, can we divide 84 chalksticks into groups of six?

Suraj : Let me divide by 6. 84 can be divided exactly by 6 and the quotient is 14. Thus, we can make 14 groups of 6. So, 84 is the multiple of 6 and 6 is a factor of 84.

Dada : If the number of chalksticks is 6, 12, 18, 36 or 84, then we can make exact groups of 6 with none left over. It means that 6, 12, 18, 36 and 84 are multiples of 6, or that they are exactly divisible by 6. To see whether the number of chalksticks is a multiple of 6, divide that number by 6. If the remainder is 0, the number is a multiple of 6.

Each number in the 3 times table is exactly divisible by 3 or is a multiple of 3. Similarly, the numbers in the 7 times table are multiples of 7. Numbers in the 9 times table are multiples of 9.

We use this idea all the time. Let me ask you a few questions so as to make it clear. I have a 200 ml measure. Will I be able to measure out 1 litre of milk with it?

Suraj : I litre is 1000 ml. 1000 = 200 × 5, which means that 1000 is a multiple of 200. So we can measure out 1 litre of milk with the 200 millilitre measure. 5 measures of 200 ml make 1 litre.

Dada : Can we measure out one and a half litres of milk with the 200 ml measure?

Anju : One and a half litres is 1500 ml. 1500 is not divisible by 200. So, it is not a multiple of 200. So the 200 ml measure cannot be used to measure out one and a half litres of milk.

Dada : I have 400 grams of chana. I have to make pouches of 60 grams each. Is that possible, if I don’t want any left overs?

Anju : No. 400 is not a multiple of 60.

Dada : How much more chana will I need to make those pouches of 60 grams each?

Anju : We will have to find the multiple of 60 that comes directly after 400. 60 × 6 = 360, 60 × 7 = 420. So, we need 20 grams more of chana.

Tests for divisibility

Study the 2 times table and see which numbers appear in the units place. Similarly, divide 52, 74, 80, 96 and 98 by 2 to see if they are exactly divisible by 2. What rule do we get for determining whether a number is a multiple of 2?

Now study the 5 and 10 times tables.

See what rules you get for finding multiples of 5 and 10, that is, numbers divisible by 5 and 10.

Test for divisibility by 2 : If there is 0, 2, 4, 6 or 8 in the units place, the number is a multiple of 2, or is exactly divisible by 2.

Test for divisibility by 5 : Any number with 5 or 0 in the units place is a multiple of 5 or, is divisible by 5.

Test for divisibility by 10 : Any number that has 0 in the units place is a multiple of 10.

Additional Important Questions and Answers

Question 1.
Write the factors of the following numbers.

(1) 45
Answer:
45 is exactly divisible by 1, 3, 5, 9,15, 45.
So, 1, 3, 5, 9, 15, 45 are the factors of 45.

(2) 48
Answer:
48 is exactly divisible by 1, 2, 3, 4, 6, 8,12,16, 24, 48.
So, 1, 2, 3, 4, 6, 8,12,16, 24, 48 are the factors of 48.

(3) 60
Answer:
60 is exactly divisible by 1, 2, 3, 4, 5, 6,10,12, 15, 20, 30, 60
So, 1, 2, 3, 4, 5, 6,10, 12, 15, 20, 30, 60 are the factors of 60.

Question 2.
Is 8 a factor of 60?
Answer:
No, since 60 is not exactly divisible by 8.

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Maharashtra Board Solutions Class 5-Maths (Problem Set 32) – Part 2: Chapter 8- Multiples and Factors

Download PDF: Maharashtra Board Solutions Class 5-Maths (Problem Set 32) – Part 2: Chapter 8- Multiples and Factors PDF

Chapterwise Maharashtra Board Solutions Class 5 Maths :

Part 1

Part 2.

FAQs

Where do I get the Maharashtra State Board Books PDF For free download?

You can download the Maharashtra State Board Books from the eBalbharti official website, i.e. cart.ebalbharati.in or from this article.

How to Download Maharashtra State Board Books?

Students can get the Maharashtra Books for primary, secondary, and senior secondary classes from here.  You can view or download the Maharashtra State Board Books from this page or from the official website for free of cost. Students can follow the detailed steps below to visit the official website and download the e-books for all subjects or a specific subject in different mediums.
Step 1: Visit the official website ebalbharati.in
Step 2: On the top of the screen, select “Download PDF textbooks” 
Step 3: From the “Classes” section, select your class.
Step 4: From “Medium”, select the medium suitable to you.
Step 5: All Maharashtra board books for your class will now be displayed on the right side. 
Step 6: Click on the “Download” option to download the PDF book.

Who developed the Maharashtra State board books?

As of now, the MSCERT and Balbharti are responsible for the syllabus and textbooks of Classes 1 to 8, while Classes 9 and 10 are under the Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE).

How many state boards are there in Maharashtra?

The Maharashtra State Board of Secondary & Higher Secondary Education, conducts the HSC and SSC Examinations in the state of Maharashtra through its nine Divisional Boards located at Pune, Mumbai, Aurangabad, Nasik, Kolhapur, Amravati, Latur, Nagpur and Ratnagiri.

About Maharashtra State Board (MSBSHSE)

The Maharashtra State Board of Secondary and Higher Secondary Education or MSBSHSE (Marathi: महाराष्ट्र राज्य माध्यमिक आणि उच्च माध्यमिक शिक्षण मंडळ), is an autonomous and statutory body established in 1965. The board was amended in the year 1977 under the provisions of the Maharashtra Act No. 41 of 1965.

The Maharashtra State Board of Secondary & Higher Secondary Education (MSBSHSE), Pune is an independent body of the Maharashtra Government. There are more than 1.4 million students that appear in the examination every year. The Maha State Board conducts the board examination twice a year. This board conducts the examination for SSC and HSC. 

The Maharashtra government established the Maharashtra State Bureau of Textbook Production and Curriculum Research, also commonly referred to as Ebalbharati, in 1967 to take up the responsibility of providing quality textbooks to students from all classes studying under the Maharashtra State Board. MSBHSE prepares and updates the curriculum to provide holistic development for students. It is designed to tackle the difficulty in understanding the concepts with simple language with simple illustrations. Every year around 10 lakh students are enrolled in schools that are affiliated with the Maharashtra State Board.