Number System - REET Maths Notes
Number System is the foundation of REET Maths - classifying natural, whole, integer and rational numbers, and the Indian numbering system, comes up at every class level. This page clarifies all the essential rules and calculations alongside REET 2024's solved questions.
- 2 questions in REET 2024
- Class 3-8 level
- 6 min read
How REET asks this topic
REET 2024 asked direct computational questions on Number System - one question required identifying all prime numbers in a given range (60 to 80) and adding them up, and another required converting a large number written in words (crore-lakh) into digits. In other words, this topic tests calculation accuracy and speed more than rote definitions, because this is exactly the foundation needed to teach maths from Class 1 to 8.
Types of numbers
| Type | Definition | Example |
|---|---|---|
| Natural numbers (N) | Numbers used for counting, starting from 1 | 1, 2, 3, 4, ... |
| Whole numbers (W) | Natural numbers + zero (0) | 0, 1, 2, 3, ... |
| Integers (Z) | Whole numbers + negative numbers | ..., -2, -1, 0, 1, 2, ... |
| Rational numbers (Q) | Numbers that can be written as p/q (q not 0) | 1/2, -3/4, 5 (=5/1) |
| Irrational numbers | Numbers that cannot be written as p/q | sqrt(2), sqrt(3), pi |
| Real numbers (R) | The set of rational + irrational numbers | -2, 0, 1/2, sqrt(2), pi |
0 is not a natural number, but it is a whole number - REET often tests this distinction.
Prime and composite numbers
A number with exactly two factors - 1 and itself - is called a prime number, such as 2, 3, 5, 7, 11. 2 is the only even prime number; every other prime is odd. A number with more than two factors is called a composite number, such as 4, 6, 8, 9. The number 1 is neither prime nor composite - an exception that is frequently misunderstood in exams.
REET 2024's question required identifying the primes between 60 and 80. In this range, 61, 67, 71, 73 and 79 are prime, while 63 (=7x9), 65 (=5x13), 69 (=3x23), 75 (=3x25) and 77 (=7x11) are composite. Their sum is 61+67+71+73+79 = 351, which is the correct answer.
Divisibility rules
| Divisible by | Rule |
|---|---|
| 2 | The units digit is 0, 2, 4, 6 or 8 |
| 3 | The sum of the digits is divisible by 3 |
| 4 | The number formed by the last two digits is divisible by 4 |
| 5 | The units digit is 0 or 5 |
| 6 | The number is divisible by both 2 and 3 |
| 8 | The number formed by the last three digits is divisible by 8 |
| 9 | The sum of the digits is divisible by 9 |
| 11 | The difference between the sum of digits at odd places and the sum at even places is 0 or a multiple of 11 |
Example: in 6534, the sum of digits at odd places (4, 5) is 9, and at even places (3, 6) is also 9; the difference is 0, so 6534 is divisible by 11.
The Indian Place Value System
In the Indian system, the place values from right to left go: units, tens, hundreds, thousands, ten thousands, lakh, ten lakh, crore. Note that lakh comes right after ten thousand - the place value between 'thousand' and 'lakh' is 'ten thousand'. When writing a number, a comma is placed after the first three digits from the right, and then after every two digits - for example, 5,52,21,305.
REET 2024's question required converting 'five crore fifty-two lakh twenty-one thousand three hundred and five' into digits. Five crore = 5,00,00,000; fifty-two lakh = 52,00,000; twenty-one thousand = 21,000; three hundred and five = 305. Adding these gives 5,52,21,305, i.e. 55221305. A digit's place value depends on both its position and its value, while its face value is always just the digit itself.
Indian vs International numbering system
International system
ThousandThousand
Ten thousandTen Thousand
LakhHundred Thousand
Ten lakhMillion
CroreTen Million
Value
Thousand1,000
Ten thousand10,000
Lakh1,00,000
Ten lakh10,00,000
Crore1,00,00,000
REET-level questions can ask you to convert between the two systems (like turning lakh into million) - 1 million = 10 lakh.
Consecutive numbers, even-odd, and successor-predecessor
Consecutive numbers are numbers that follow one after another in sequence, like 7, 8, 9. The successor of a number is found by adding 1 to it, and the predecessor by subtracting 1 - for example, the successor of 20 is 21 and its predecessor is 19.
Numbers that are exactly divisible by 2 are called even (like 2, 4, 6), and those that aren't are called odd (like 1, 3, 5). Any two consecutive even numbers, or any two consecutive odd numbers, always differ by 2 - REET uses exactly this rule to set up equations like 'x, x+2'.
How to teach this to children
Classroom activity
In Classes 1-3, use bundles of ten ice-cream sticks or matchsticks to teach place value - one bundle = tens, ten bundles = hundreds. This helps children understand 'tens' and 'hundreds' by counting them, not just memorising the terms.
Teaching aids
Hang a place-value chart on the board with columns for units, tens, hundreds, thousands, etc. - have children write each number into these columns and read it back.
Common misconception
Children often think 0 is a natural number, or that 1 is prime. Clear up both misconceptions repeatedly with examples - 1 has only one factor (itself), so it is neither prime nor composite.
Assessment idea
Show children large numbers from a market receipt or newspaper (like population figures) and have them practise reading them in words and writing them in digits - this connects the concept to real life.
Trick to remember / exam tip
To place commas in a large number, start counting from the right: one comma after the first 3 digits, then one comma after every 2 digits from there - for example, write 705042311 as 70,50,42,311. Remember this pattern (3-2-2-2...) and word-to-digit questions will never go wrong.
Questions asked in REET 2024 (with solutions)
Question 95
The sum of all prime numbers between 60 and 80 is
- A291
- B351
- C434
- D373
Explanation
60 और 80 के बीच अभाज्य संख्याएँ हैं: 61, 67, 71, 73, 79। इनका योग = 61 + 67 + 71 + 73 + 79 = 351। ध्यान दें कि 63, 69, 77 आदि अभाज्य नहीं हैं (क्रमशः 3, 3, 7 से विभाज्य)।
Question 99
The numerical form of five crore fifty two lakh twenty one thousand three hundred five is
- A52521305
- B55221305
- C53052125
- D52152305
Explanation
पाँच करोड़ = 5,00,00,000; बावन लाख = 52,00,000; इक्कीस हजार = 21,000; तीन सौ पाँच = 305। इन्हें जोड़ने पर भारतीय पद्धति में 5,52,21,305 अर्थात् 55221305 प्राप्त होता है।
Practice Questions
Question 1
Which of the following is not a natural number?
- A1
- B0
- C5
- D100
Explanation
Natural numbers start from 1. 0 is not a natural number - it is a whole number.
Question 2
Which is the smallest composite number?
- A1
- B2
- C4
- D9
Explanation
1 is neither prime nor composite, 2 is the smallest prime number. 4 has three factors (1, 2, 4), so it is the smallest composite number.
Question 3
Which of the following numbers is exactly divisible by 11?
- A6431
- B6534
- C6635
- D6745
Explanation
In 6534, the sum of digits at odd places (4, 5) equals the sum at even places (3, 6) - both are 9 - so the difference is zero, and 6534 is divisible by 11 (6534 / 11 = 594). The other three numbers don't have this difference as 0 or a multiple of 11.
Question 4
What is the largest two-digit prime number?
- A91
- B93
- C97
- D99
Explanation
91=7x13, 93=3x31, 99=9x11 - all three are composite. None of 2, 3, 5 or 7 divides 97, so it is prime, and it is the largest two-digit prime number.
Question 5
In the Indian place-value system, the 'lakh' place comes immediately after which place?
- Aदस हज़ार
- Bकरोड़
- Cदस लाख
- Dहज़ार
Explanation
In the Indian system, the order is: units, tens, hundreds, thousands, ten thousands, lakh, ten lakh, crore. So the 'lakh' place comes right after 'ten thousand'.
Question 6
In the number 7,05,04,231, what is the place value of the digit '5'?
- A5,000
- B50,000
- C5,00,000
- D50,00,000
Explanation
In this number, '5' is in the lakh place (7 crore, 0 ten-lakh, 5 lakh...), so its place value is 5 x 1,00,000 = 5,00,000.
Question 7
How many prime numbers are there among the positive integers from 1 to 20?
- A6
- B7
- C8
- D9
Explanation
The primes between 1 and 20 are: 2, 3, 5, 7, 11, 13, 17, 19 - 8 numbers in total.
Question 8
The sum of two consecutive odd numbers is 44. What is the smaller number?
- A19
- B21
- C23
- D25
Explanation
Let the numbers be x and x+2. Then 2x+2=44, so x=21. The smaller number is 21 and the larger is 23.
Question 9
When a number is divided by 7, the quotient is 15 and the remainder is 4. What is the number?
- A105
- B109
- C111
- D115
Explanation
Number = divisor x quotient + remainder = 7 x 15 + 4 = 105 + 4 = 109.
Question 10
Which is the most suitable teaching aid for a teacher to explain the concept of place value to Class 3 students?
- Aदस-दस की गड्डियों (बंडल) और स्थानीय मान चार्ट का प्रयोग
- Bकेवल श्यामपट्ट पर संख्याएँ लिखना
- Cपरीक्षा के पुराने प्रश्नपत्र हल कराना
- Dकेवल मौखिक व्याख्यान देना
Explanation
Concrete material (bundles of ten, place-value charts) is the most effective way to teach an abstract concept like place value in the early grades, because children learn best by counting and seeing.
Frequently Asked Questions
How many questions come from Number System in REET?+
REET 2024 had 1-2 questions from this topic in the Maths section, based on direct calculation (primes, converting large numbers).
Is 0 a natural number?+
No, 0 is not a natural number. It falls under whole numbers, since whole numbers = natural numbers + 0.
Is 1 a prime number?+
No. 1 has only one factor (itself), so it is neither prime nor composite - it's a special case.
Which is the smallest composite number?+
4 is the smallest composite number, since it has three factors - 1, 2 and 4.
What's the difference between an integer and a rational number?+
Integers (like -2, 0, 5) have no decimal or fractional part, while a rational number can be any number of the form p/q, which includes fractions (like 1/2) - every integer is a rational number, but not every rational number is an integer.
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Change Log
- 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked