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Number Play – Class 7 Mathematics notes, important questions and MCQs

NCERT Class 7 Mathematics, chapter 6. Notes, key terms, important questions with answers and MCQs.

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Chapter overview

Patterns in numbers — odd and even, factors, multiples and digit sums — help solve puzzles and check calculations.

Odd, even and parity

Even + even = even; odd + odd = even; even + odd = odd.
Odd × odd = odd; anything × even = even.
Sum of first n odd numbers = n².

Factors and multiples

A factor divides a number exactly; a multiple is the number times a whole number.
Prime numbers have exactly two factors; 1 is neither prime nor composite.
HCF is the highest common factor; LCM is the lowest common multiple.

Key terms

Parity: whether a number is odd or even
Prime number: number with exactly two factors, 1 and itself
LCM: smallest number that is a multiple of each given number

Formulas

1 + 3 + 5 + … (n terms) = n²
HCF × LCM = product of two numbers

Important questions with answers

Is the sum of three odd numbers odd or even? Why?2 marks

Odd. Two odd numbers add to even, and even + odd = odd.

Find the LCM of 12 and 18, and use it to find when two bells ringing every 12 and 18 minutes ring together again.3 marks

12 = 2² × 3, 18 = 2 × 3², LCM = 2² × 3² = 36. They ring together again after 36 minutes.

In a 3 × 3 magic square using 1 to 9, what is the magic sum and which number must be in the centre? Make one such square.5 marks

Total of 1 to 9 = 45, shared by 3 rows, so each row, column and diagonal adds to 15. The centre must be 5. One square: rows 2 7 6 / 9 5 1 / 4 3 8 (check: 2 + 7 + 6 = 15, 2 + 5 + 8 = 15, 6 + 5 + 4 = 15).

Quick revision

Odd + odd = even.
1 is neither prime nor composite.
HCF divides LCM.

Exam tips

Use parity to reject impossible answers quickly.
2 is the only even prime.

Practice MCQs

Sum of two odd numbers is always
1. even
2. odd
3. prime
4. zero
Show answer
Answer: (a) even. e.g. 3 + 5 = 8.
Which is a prime number?
1. 21
2. 27
3. 29
4. 33
Show answer
Answer: (c) 29. Only factors 1 and 29.
HCF of 18 and 24 is
1. 3
2. 6
3. 12
4. 72
Show answer
Answer: (b) 6. Common factors 1, 2, 3, 6.
LCM of 6 and 8 is
1. 24
2. 48
3. 14
4. 2
Show answer
Answer: (a) 24. Smallest common multiple.
The sum of two odd numbers is always
1. even
2. odd
3. prime
4. zero
Show answer
Answer: (a) even. Odd + odd = even.
Sum of the first 15 odd numbers is
1. 196
2. 210
3. 225
4. 256
Show answer
Answer: (c) 225. 15².
Can the sum of 5 odd numbers be 50?
1. yes
2. no
3. only if one is 1
4. only if they are equal
Show answer
Answer: (b) no. Odd count of odd numbers gives an odd sum.
The smallest number divisible by 4, 6 and 10 is
1. 30
2. 60
3. 120
4. 240
Show answer
Answer: (b) 60. LCM = 60.

All chapters of Class 7 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.