Maharashtra Board Solutions Class 5-Maths (Problem Set 35) - 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 35) - Part 2: Chapter 8- Multiples and Factors

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

Important Questions and Answers.

Determine whether the pairs of numbers given below are co-prime numbers.
(1) 22, 24
Answer:
Common factors of 22 and 24 are 1 and 2. (Not only 1 common factor) So, 22, 24 are not co-prime numbers.

(2) 14, 21
Answer:
Common factors of 14 and 21 are 1 and 7. So, this pair is not co-prime numbers.

(3) 10, 33
Answer:
Common factors of 10 and 33 is only 1. So, 10 and 33 are co-prime numbers.

(4) 11, 30
Answer:
Common factors of 11 and 30 is only 1. So, 11 and 30 are co-prime numbers.

(5) 5, 7
Answer:
Common factor of 5 and 7 is only 1. So, 5 and 7 are co-prime numbers.

(6) 15, 16
Answer:
Common factors of 15 and 16 is only 1. So, 15 and 16 are co-prime numbers.

(7) 50, 52
Answer:
Common factors of 50 and 52 are 1 and 2. So, 50 and 52 are not co-prime numbers.

(8) 17, 18
Answer:
Common factors of 17 and 18 is only 1. So, 17 and 18 are co-prime numbers.

Activity 1 :

• Write numbers from 1 to 60.
• Draw a blue circle around multiples of 2.
• Draw a red circle around multiples of 4.
• Do all numbers with a blue circle also have a red circle around them?
• Do all the numbers with a red circle have a blue circle around them?
• Are all multiples of 2 also multiples of 4?
• Are all multiples of 4 also multiples of 2?

Activity 2 :

• Write numbers from 1 to 60.
• Draw a triangle around multiples of 2.
• Draw a circle around multiples of 3.
• Now find numbers divisible by 6. Can you find a property that they share?

Eratosthenes’ method of finding prime numbers
Eratosthenes was a mathematician who lived in Greece about 250 BC. He discovered a method to find prime numbers. It is called Eratosthenes’ Sieve. Let us see how to find prime numbers between 1 and 100 with this method.

• 1 is neither a prime nor a composite number. Put a square [ ] around it
• 2 is a prime number, so put a circle around it.
• Next, strike out all the multiples of 2. This tells us that of these 100 numbers more than half of numbers are not prime numbers.
• The first number after 2 not yet struck off is 3. So, 3 is a prime number.
• Draw a circle around 3. Strike out all the multiples of 3.
• The next number after 3 not struck off yet is 5. So, 5 is a prime number.
• Draw a circle around 5. Put a line through all the multiples of 5.
• The next number after 5 without a line through it is 7. So, 7 is a prime number.
• Draw a circle around 7. Put a line through all the multiples of 7.

In this way, every number between 1 and 100 will have either a circle or a line through it. The circled numbers are prime numbers. The numbers with a line through them are composite numbers.

One more method to find prime numbers

See how numbers from 1 to 36 have been arranged in six columns in the table alongside.

Continue in the same way and write numbers up to 102 in these six columns.

You will see that, in the columns for 2, 3, 4, and 6, all the numbers are composite numbers except for the prime numbers 2 and 3. This means that all the remaining prime numbers will be in the columns for 1 and 5. Now isn’t it easier to find them? So, go ahead, find the prime numbers!

Something more

• Prime numbers with a difference of two are called twin prime numbers. Some twin prime number pairs are 3 and 5, 5 and 7, 29 and 31 and 71 and 73. 5347421 and 5347423 are also a pair of twin prime numbers.
• There are eight pairs of twin prime numbers between 1 and 100. Find them.
• Euclid the mathematician lived in Greece about 300 BC. He proved that if prime numbers, 2, 3, 5, 7, ……., are written in serial order, the list will never end, meaning that the number of prime numbers is infinite.

Additional Important Questions and Answers

Determine whether the pairs of numbers given below are co-prime numbers.

(1) (12,18)
Answer:
Common factors of 12 and 18 are 1, 2, 3, 6. Hence 12 and 18 are not co-prime numbers.

(2) (26, 39)
Answer:
Common factors of 26 and 39 are 1 and 13. Hence, 26 and 39 are not co-prime numbers.

(3) (23, 29)
Answer:
Common factor of 23 and 29 is only 1. Hence, 23 and 29 are co-prime numbers.

(4) (28, 32)
Answer:
Common factors of 28 and 32 are 1, 2, 4 (not only 1). Hence, 28, 32 are not co-prime numbers.

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Maharashtra Board Solutions Class 5-Maths (Problem Set 35) - Part 2: Chapter 8- Multiples and Factors

Download PDF: Maharashtra Board Solutions Class 5-Maths (Problem Set 35) - Part 2: Chapter 8- Multiples and Factors PDF

Chapterwise Maharashtra Board Solutions Class 5 Maths :

Part 1

• Chapter 1- Roman Numerals (Problem Set 1)
• Chapter 2- Number Work (Problem Set 2)
• Chapter 2- Number Work (Problem Set 3)
• Chapter 2- Number Work (Problem Set 4)
• Chapter 2- Number Work (Problem Set 5)
• Chapter 2- Number Work (Problem Set 6)
• Chapter 3- Addition and Subtraction (Problem Set 7)
• Chapter 3- Addition and Subtraction (Problem Set 8)
• Chapter 3- Addition and Subtraction (Problem Set 9)
• Chapter 3- Addition and Subtraction (Problem Set 10)
• Chapter 3- Addition and Subtraction (Problem Set 11)
• Chapter 3- Addition and Subtraction (Problem Set 12)
• Chapter 3- Addition and Subtraction (Problem Set 13)
• Chapter 4- Multiplication and Division (Problem Set 14)
• Chapter 4- Multiplication and Division (Problem Set 15)
• Chapter 4- Multiplication and Division (Problem Set 16)
• Chapter 5- Fractions (Problem Set 17)
• Chapter 5- Fractions (Problem Set 18)
• Chapter 5- Fractions (Problem Set 19)
• Chapter 5- Fractions (Problem Set 20)
• Chapter 5- Fractions (Problem Set 21)
• Chapter 5- Fractions (Problem Set 22)
• Chapter 5- Fractions (Problem Set 23)
• Chapter 6- Angles (Problem Set 24)
• Chapter 6- Angles (Problem Set 25)
• Chapter 6- Angles (Problem Set 26)
• Chapter 6- Angles (Problem Set 27)
• Chapter 7- Circles (Problem Set 28)
• Chapter 7- Circles (Problem Set 29)
• Chapter 7- Circles (Problem Set 30)
• Chapter 7- Circles (Problem Set 31)

Part 2.

• Chapter 8- Multiples and Factors (Problem Set 32)
• Chapter 8- Multiples and Factors (Problem Set 33)
• Chapter 8- Multiples and Factors (Problem Set 34)
• Chapter 8- Multiples and Factors (Problem Set 35)
• Chapter 9- Decimal Fractions (Problem Set 36)
• Chapter 9- Decimal Fractions (Problem Set 37)
• Chapter 9- Decimal Fractions (Problem Set 38)
• Chapter 9- Decimal Fractions (Problem Set 39)
• Chapter 9- Decimal Fractions (Problem Set 40)
• Chapter 9- Decimal Fractions (Problem Set 41)
• Chapter 9- Decimal Fractions (Problem Set 42)
• Chapter 10- Measuring Time (Problem Set 43)
• Chapter 10- Measuring Time (Problem Set 44)
• Chapter 10- Measuring Time (Problem Set 45)
• Chapter 11- Problems on Measurement (Problem Set 46)
• Chapter 11- Problems on Measurement (Problem Set 47)
• Chapter 12- Perimeter and Area (Problem Set 48)
• Chapter 12- Perimeter and Area (Problem Set 49)
• Chapter 12- Perimeter and Area (Problem Set 50)
• Chapter 13- Three Dimensional Objects and Nets (Problem Set 51)
• Chapter 14- Pictographs (Problem Set 52)
• Chapter 15- Patterns (Problem Set 53)
• Chapter 16- Preparation for Algebra (Problem Set 54)
• Chapter 16- Preparation for Algebra (Problem Set 55)
• Chapter 16- Preparation for Algebra (Problem Set 56)