SAT Number Properties: A Guide to Core Skills

Number properties form the foundation for many questions in the SAT Math section. This guided path will teach you the essential concepts you need to solve problems involving integers, factors, and divisibility with speed and accuracy.

Section 1: Number Classification & Core Concepts

The Building Blocks: Number Classification

Start with the fundamental types of numbers. This is the basic vocabulary for all Number Properties questions.

Classification Hierarchy

  • Real Numbers[-]
    All types below
    • Rational[-]
      5, 2.7, -92.4, 22/7
      • Integers[-]
        ..., -2, -1, 0, 1, 2, ...
        • Natural
          1, 2, 3...
        • Whole
          0, 1, 2, 3...
      • Fractions
        1/2, -7/3, 2.75
    • Irrational
      √2, √3, π, e

Real Numbers

All rational and irrational numbers. They can be represented on a continuous number line.

Examples
All types below

Number Line Visualization

-3
-2
-1
0
1
2
3

Hover over points to see values.

Integer Properties: Prime, Even & Odd

Dive deeper into the most important number type—integers. Learn what makes them Prime, Even, Odd, and more with interactive examples.

Further Classifications of Integers

💡 Key Takeaways

  • 1 is neither Prime nor Composite.
  • 2 is the only Even Prime number.
  • There are 25 Prime numbers between 1 and 100.

Odd & Even Calculation Properties

Master the rules for adding, subtracting, and multiplying odd and even numbers—a key skill for logical deduction and checking your work.

Addition Rules

+
=
?

Section 2: Core SAT Skills & Problem Solving

Divisibility: A Complete Guide

Master the essential rules of divisibility. This is a critical time-saving skill for the no-calculator section.

Rule for 3
If the sum of all digits is divisible by 3, so is the number.
Rule for 4
If the number formed by the last 2 digits is divisible by 4, so is the original number.
Rule for 5
Ends in 0 or 5.
Rule for 6
Must be divisible by BOTH 2 (even) and 3.
Rule for 8
If the number formed by the last 3 digits is divisible by 8.
Rule for 9
If the sum of all digits is divisible by 9.
Rule for 11
Difference between sum of digits in odd positions and sum of digits in even positions is 0 or multiple of 11.

Factors & HCF: Interactive Tools

Learn about prime factorization and how to find the Highest Common Factor (HCF) of two numbers.

Prime Factorization

Every integer > 1 is a unique product of primes.
e.g., 12 = 2² × 3

Total Factors Formula

If N = aᵖ × b^q, Total Factors = (p+1)(q+1).

Interactive Practice

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Expert Strategy & Insights

The 'Symmetric Sequence' Trick for Standard Deviation

The 'Symmetric Sequence' Trick for Standard Deviation

Stop calculating! Learn how to use the properties of symmetry to solve hard SD questions in seconds.