Number System — SSC GD Study Notes

Overview

The Number System is the foundation of all mathematics tested in SSC GD. This topic covers whole numbers (0, 1, 2, 3…), integers (including negative numbers), place value concepts, and divisibility rules. Expect 3–5 direct questions from this area in every paper, plus countless indirect applications in arithmetic and reasoning sections.

Mastery here means you can quickly identify whether a number is divisible by 2, 3, 5, 7, 9, or 11 without performing division, understand place values in multi-digit numbers, and confidently work with positive and negative integers. These skills speed up your calculations in percentage, average, and simplification problems—making this topic a force multiplier for your entire math score.

The exam tests practical number sense: comparing numbers, ordering them, applying divisibility shortcuts, and manipulating place values. Focus on speed and accuracy—these are warm-up questions you must solve in under 30 seconds each to bank time for harder problems later.

Key Concepts

• **Whole Numbers** include 0, 1, 2, 3, 4… extending infinitely. They represent counts and cannot be negative or fractional.

• **Integers** expand whole numbers to include negatives: …−3, −2, −1, 0, 1, 2, 3… Every whole number is an integer, but not vice versa.

• **Place Value** determines a digit's worth by its position: in 4,573, the 5 represents 500 (5 hundreds), not just 5. Right-to-left positions are ones, tens, hundreds, thousands, etc.

• **Face Value** is the digit itself regardless of position. In 4,573, the face value of 5 is always 5.

• **Divisibility Rules** let you test whether one number divides another evenly without performing full division—critical for speed.

• **Even numbers** end in 0, 2, 4, 6, or 8 and are divisible by 2. **Odd numbers** end in 1, 3, 5, 7, or 9.

• **Prime numbers** (2, 3, 5, 7, 11, 13…) have exactly two factors: 1 and themselves. The number 1 is not prime; 2 is the only even prime.

• **Composite numbers** have more than two factors. Examples: 4, 6, 8, 9, 10. Every integer greater than 1 is either prime or composite.

Formulas / Key Facts

**Divisibility Rules:**

• **By 2:** Last digit is 0, 2, 4, 6, or 8.
• **By 3:** Sum of all digits is divisible by 3. (Example: 573 → 5+7+3=15, 15÷3=5, so 573 is divisible by 3)
• **By 4:** Last two digits form a number divisible by 4. (Example: 816 → 16÷4=4, so 816 is divisible by 4)
• **By 5:** Last digit is 0 or 5.
• **By 6:** Divisible by both 2 and 3 simultaneously.
• **By 8:** Last three digits form a number divisible by 8.
• **By 9:** Sum of all digits is divisible by 9. (Example: 729 → 7+2+9=18, 18÷9=2, so 729 is divisible by 9)
• **By 10:** Last digit is 0.
• **By 11:** Difference between sum of digits at odd positions and sum at even positions is 0 or divisible by 11. (Example: 1331 → (1+3) − (3+1) = 0, so divisible by 11)

**Place Value:**

• A number like 6,483 = 6×1000 + 4×100 + 8×10 + 3×1 = 6000 + 400 + 80 + 3.

**Properties of Zero and One:**

• 0 is an integer and whole number, but not positive or negative.
• 1 is the multiplicative identity: any number × 1 = that number.
• 0 is the additive identity: any number + 0 = that number.

**Number of digits in a number:**

• Single-digit: 1–9 (9 numbers)
• Two-digit: 10–99 (90 numbers)
• Three-digit: 100–999 (900 numbers)

Worked Examples

**Example 1: Check divisibility of 5,832 by 3, 4, and 8.**

*Step 1 — Divisibility by 3:* Sum of digits = 5+8+3+2 = 18. 18 ÷ 3 = 6, so 5,832 **is divisible by 3**.

*Step 2 — Divisibility by 4:* Last two digits = 32. 32 ÷ 4 = 8, so 5,832 **is divisible by 4**.

*Step 3 — Divisibility by 8:* Last three digits = 832. 832 ÷ 8 = 104, so 5,832 **is divisible by 8**.

**Answer:** 5,832 is divisible by 3, 4, and 8.

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**Example 2: Find the place value and face value of 7 in 37,492.**

*Step 1 — Identify position:* 37,492 → The 7 is in the thousands place.

*Step 2 — Calculate place value:* Place value = 7 × 1000 = 7,000.

*Step 3 — Face value:* Face value = 7 (always the digit itself).

**Answer:** Place value = 7,000; Face value = 7.

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**Example 3: Test whether 4,235 is divisible by 11.**

*Step 1 — Identify odd and even positions:* Positions from right: 5(1st), 3(2nd), 2(3rd), 4(4th). Odd positions (1st, 3rd): 5 + 2 = 7. Even positions (2nd, 4th): 3 + 4 = 7.

*Step 2 — Find difference:* Difference = 7 − 7 = 0.

*Step 3 — Apply rule:* 0 is divisible by 11, so 4,235 **is divisible by 11**.

**Answer:** Yes, divisible by 11.

Common Mistakes

**Mistake 1: Confusing face value with place value.** Wrong thinking: "In 5,430, the face value of 4 is 400." Correct fix: Face value is always the digit itself (4). Place value is 400.

**Mistake 2: Forgetting zero is not positive or negative.** Wrong thinking: "0 is a positive whole number." Correct fix: 0 is neutral—neither positive nor negative. It is a whole number and an integer.

**Mistake 3: Misapplying the divisibility rule for 11.** Wrong thinking: "Sum all digits and check divisibility by 11." Correct fix: Find the *difference* between the sum of digits at odd positions and even positions, then check if that difference is 0 or divisible by 11.

**Mistake 4: Thinking 1 is a prime number.** Wrong thinking: "1 is the smallest prime." Correct fix: A prime has exactly two distinct factors. 1 has only one factor (itself), so 1 is neither prime nor composite. The smallest prime is 2.

**Mistake 5: Testing only the last digit for divisibility by 4 or 8.** Wrong thinking: "628 ends in 8, so divisible by 4." Correct fix: For 4, check the last *two* digits (28 ÷ 4 = 7, so yes). For 8, check the last *three* digits. The final digit alone is not enough.

Quick Reference

• Whole numbers start at 0 and go up: 0, 1, 2, 3… Integers include negatives too.
• Divisibility by 2, 5, 10: check the last digit only.
• Divisibility by 3, 9: sum all digits and test the sum.
• Divisibility by 4: last two digits; by 8: last three digits.
• Divisibility by 11: (sum of odd-position digits) − (sum of even-position digits) = 0 or multiple of 11.
• Place value = digit × positional value (tens, hundreds, etc.); face value = digit itself.