Important Formulas: Animal Jumps | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

Introduction

• Numbers follow special patterns.

• Factors break numbers into smaller exact parts.

• Multiples show how numbers grow bigger when multiplied.

• Learning factors and multiples makes it easier to understand divisibility, prime numbers, and patterns in mathematics.

Factors

A factor of a number divides it exactly without leaving a remainder.

• If a × b = N, then both a and b are factors of N.

Examples

Factors of 8:
1 × 8 = 8, 2 × 4 = 8
∴ Factors = 1, 2, 4, 8

Rules

1. Every number has at least two factors: 1 and the number itself.

2. Factors are always less than or equal to the number.

3. Factors come in pairs (factor pairs).

Finding Factors

1. Start with 1 and the number itself.

2. Check each number in between.

3. If the division leaves no remainder, it is a factor.

Common Factors

If two or more numbers share the same factor → common factor.

Example:

• Factors of 12 = 1, 2, 3, 4, 6, 12

• Factors of 18 = 1, 2, 3, 6, 9, 18

• Common factors = 1, 2, 3, 6

Another Example:

• Common factors = 1, 2, 3, 6

Prime and Composite Numbers

1. Prime Numbers → Numbers with exactly two factors: 1 and itself.

   • Example: 13 (factors: 1, 13)

2. Composite Numbers → Numbers with more than two factors.

   • Example: 4 (factors: 1, 2, 4)

3. Special Case:

   • 1 is neither prime nor composite.

Multiples

A multiple of a number = product of the number × any counting number.

Example: Multiples of 3:
3, 6, 9, 12, 15, 18, …

Rules

1. Every number is a multiple of 1.

2. The smallest multiple of a number is the number itself.

3. Multiples are infinite.

4. Every multiple is greater than or equal to the number.

Finding Multiples

• Multiply the number by 1, 2, 3, 4, …

Common Multiples

When two or more numbers share a multiple → common multiple.

Example:

• Multiples of 3 = 3, 6, 9, 12, 15, …

• Multiples of 4 = 4, 8, 12, 16, …

• Common multiples = 12, 24, 36, …

Another Example: 

Common multiples = 24, 48, …

Divisibility Rules

Quick tests to check divisibility without long division:

1. By 2 → Last digit 0, 2, 4, 6, 8

2. By 3 → Sum of digits divisible by 3

3. By 4 → Last two digits divisible by 4

4. By 5 → Last digit 0 or 5

5. By 6 → Divisible by both 2 and 3

6. By 8 → Last three digits divisible by 8

7. By 9 → Sum of digits divisible by 9

8. By 10 → Last digit 0

9. By 11 → (Sum of odd place digits − sum of even place digits) divisible by 11

10. By 25 → Last two digits divisible by 25