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NMAT Number Properties Formulas PDF
Number Properties is one of the most important and frequently tested topics in the NMAT Quantitative Skills section. Questions based on divisibility, remainders, factors, multiples, LCM-HCF, unit digits, and logarithms regularly appear in the exam. Since NMAT is a speed-based test, knowing the right formulas and shortcuts can help you solve questions within seconds and improve your overall score.
This article covers all the important NMAT Number Properties formulas, concepts, shortcuts, question trends, and preparation tips you need for effective revision.
Importance of NMAT Number Properties Formulas
Number Properties forms the foundation of many Quantitative Skills topics in NMAT. Mastering these formulas offers several advantages:
- Helps solve questions faster with minimum calculations.
- Frequently appears as a standalone topic in NMAT.
- Concepts are useful in percentages, ratios, algebra, and Data Interpretation.
- Unit digit and divisibility shortcuts help eliminate options quickly.
- Reduces calculation errors during the exam.
- Improves accuracy in high-weightage arithmetic questions.
A strong command of Number Properties can significantly boost your NMAT score.
Read Also, NMAT Formulas PDF, Download NMAT Quant Important Formulas
Complete NMAT Number Properties Formula List
Basics of Numbers
Types of Numbers
- Natural Numbers: 1, 2, 3, 4, ...
- Whole Numbers: 0, 1, 2, 3, ...
- Integers: ..., -3, -2, -1, 0, 1, 2, ...
- Rational Numbers: p/q where q ≠ 0
- Irrational Numbers: √2, π, etc.
- Real Numbers: Rational + Irrational
- Prime Numbers: Numbers having exactly two factors (2, 3, 5, 7...)
- Composite Numbers: Numbers having more than two factors
Important Properties
- Any number × 0 = 0
- Division by 0 is undefined
- Any number × 1 = same number
- Any non-zero number raised to power 0 = 1
- 1 is neither prime nor composite
Formula 1: Sum of First n Natural Numbers
Formula:
n(n + 1)/2
Example:
Sum of first 30 natural numbers
= 30 × 31 / 2
= 465
Formula 2: Sum of First n Odd Numbers
Formula:
n²
Example:
1 + 3 + 5 + 7
= 4²
= 16
Formula 3: Sum of First n Even Numbers
Formula:
n(n + 1)
Example:
2 + 4 + 6
= 3 × 4
= 12
Fractions
Formula 4: Addition and Subtraction of Fractions
Formula:
(a/b) ± (c/d) = (ad ± bc)/bd
Example:
2/3 + 3/5
= (10 + 9)/15
= 19/15
Formula 5: Fraction to Percentage
Formula:
Percentage = Fraction × 100
Example:
7/8 × 100
= 87.5%
Shortcut: Comparing Fractions
Compare:
a/b and c/d
Check:
a × d and c × b
Example:
5/7 vs 4/6
5 × 6 = 30
4 × 7 = 28
Therefore, 5/7 is larger.
Formula 6: Recurring Decimal to Fraction
Formula:
Repeated Digits / 99...9
Examples:
0.666...
= 6/9
= 2/3
0.181818...
= 18/99
= 2/11
Decimals
Formula 7: Decimal to Percentage
Formula:
Decimal × 100%
Example:
0.075
= 7.5%
Formula 8: Decimal Shift Rule
Multiplying by 10ⁿ moves the decimal point n places right.
Dividing by 10ⁿ moves it n places left.
Example:
3.47 × 100
= 347
3470 ÷ 1000
= 3.47
Read Also, NMAT Syllabus 2026 PDF, Section Wise Important Topics
Quick Multiplication Tricks
Multiply by 5
Divide by 2 and multiply by 10.
Multiply by 25
Divide by 4 and multiply by 100.
Multiply by 50
Divide by 2 and multiply by 100.
Example:
48 × 25
= 48 ÷ 4 × 100
= 12 × 100
= 1200
Read Also, NMAT Marking Scheme 2026, Exam Pattern, Duration
Terminating Decimal Rule
A fraction p/q terminates only if q contains prime factors 2 and/or 5 only.
Examples:
- 7/20 → Terminating
- 1/6 → Non-terminating recurring
Divisibility Rules
Number | Divisibility Test |
2 | Last digit even |
3 | Sum of digits divisible by 3 |
4 | Last two digits divisible by 4 |
5 | Ends with 0 or 5 |
6 | Divisible by both 2 and 3 |
8 | Last three digits divisible by 8 |
9 | Sum of digits divisible by 9 |
11 | Difference of alternate digit sums divisible by 11 |
25 | Last two digits are 00, 25, 50, or 75 |
Example
Find the least number to be added to 7264 to make it divisible by 9.
Digit sum = 7 + 2 + 6 + 4 = 19
Next multiple of 9 = 27
Required addition = 27 - 19
= 8
Unit Digits
Unit Digit Cycles
Base | Cycle |
2 | 2,4,8,6 |
3 | 3,9,7,1 |
4 | 4,6 |
5 | 5 |
6 | 6 |
7 | 7,9,3,1 |
8 | 8,4,2,6 |
9 | 9,1 |
Formula 9: Unit Digit of a Power
Find:
Exponent mod Cycle Length
Then choose the corresponding term.
Example
Find unit digit of 7²²²
Cycle = 7,9,3,1
222 mod 4 = 2
Second term = 9
Answer = 9
Factors
Formula 10: Number of Factors
If:
n = pᵃ × qᵇ × rᶜ
Then:
Number of Factors
= (a+1)(b+1)(c+1)
Example
72 = 2³ × 3²
Factors
= (3+1)(2+1)
= 12
Formula 11: Sum of Factors
For:
n = pᵃ × qᵇ
Sum of Factors
= [(pᵃ⁺¹ − 1)/(p − 1)] × [(qᵇ⁺¹ − 1)/(q − 1)]
Example
12 = 2² × 3
Sum of Factors
= 28
Perfect Square Shortcut
A number is a perfect square only if every exponent in its prime factorization is even.
Example
180 = 2² × 3² × 5¹
Since exponent of 5 is odd,
180 is not a perfect square.
Multiples
Formula 12: nth Multiple
nth Multiple = n × k
where k is the number.
Example
7th multiple of 14
= 7 × 14
= 98
LCM
Formula 13: Prime Factor Method
LCM is obtained by taking the highest powers of all prime factors.
Example
60 = 2² × 3 × 5
84 = 2² × 3 × 7
LCM
= 2² × 3 × 5 × 7
= 420
Formula 14: Product Relation
LCM × HCF = Product of Numbers
Example
18 and 24
HCF = 6
LCM = (18 × 24)/6
= 72
HCF
Formula 15: Euclid's Algorithm
HCF(a,b)
= HCF(b, a mod b)
Example
HCF(48,18)
48 ÷ 18 → remainder 12
18 ÷ 12 → remainder 6
12 ÷ 6 → remainder 0
HCF = 6
Formula 16: HCF-LCM Relation
a × b = HCF × LCM
Example
42 × 56 = HCF × 168
HCF = 14
Logarithms
Formula 17: Definition
logᵦa = c
if
bᶜ = a
Example
log₂8 = 3
Formula 18: Product Rule
log(MN)
= log M + log N
Formula 19: Quotient Rule
log(M/N)
= log M − log N
Formula 20: Power Rule
log(Mᵏ)
= k log M
Formula 21: Change of Base Formula
logᵦa
= logₖa / logₖb
Example
log₂10
= log10/log2
≈ 3.322
NMAT Number Properties Question Distribution
Subtopic | Expected Questions |
Divisibility & Remainders | 2-3 |
LCM & HCF | 2-3 |
Factors | 1-2 |
Unit Digits | 1-2 |
Fractions & Decimals | 1-2 |
Logarithms | 1 |
Number Basics | 1 |
Key Trends
- Divisibility and remainder questions appear almost every year.
- LCM-HCF is frequently asked through word problems.
- Unit digit questions are becoming increasingly common.
- Factor-based questions often involve counting factors.
- Logarithm questions are usually formula-based and straightforward.
Tips to Master NMAT Number Properties Formulas
1. Memorize divisibility rules thoroughly.
2. Learn unit digit cycles by heart.
3. Practice LCM-HCF shortcuts daily.
4. Solve remainder-based questions regularly.
5. Revise factor formulas weekly.
6. Understand logarithm identities instead of memorizing them mechanically.
7. Create a one-page formula sheet for revision.
8. Solve previous NMAT Number Properties questions topic-wise.
9. Focus on speed along with accuracy.
10. Revise weak areas during the last two weeks before the exam.
Download NMAT Number Properties Formulas PDF
A well-structured formula PDF can significantly improve your revision speed before the exam. The NMAT Number Properties Formula PDF includes:
- All 21 important formulas
- Divisibility rules
- Unit digit cycles
- LCM-HCF shortcuts
- Factor formulas
- Logarithm rules
- Quick revision notes
- Exam-oriented examples
Use the PDF during your final revision phase to strengthen concepts and improve recall speed before NMAT.
NMAT Number Properties Formulas PDF: Conclusion
NMAT Number Properties Formulas PDF is one of the most valuable revision resources for candidates preparing for the Quantitative Skills section. Since Number Properties covers core concepts such as divisibility, factors, multiples, LCM-HCF, unit digits, fractions, decimals, and logarithms, mastering these formulas can significantly improve both speed and accuracy in the exam.
Regular revision of the NMAT Number Properties Formulas PDF, combined with consistent practice of previous year questions and mock tests, can help candidates strengthen their fundamentals and perform confidently on exam day. Focus on understanding concepts rather than memorizing formulas blindly, and you'll be well-prepared to maximize your NMAT score.
