A number multiplied by 4 gives 64. That number is square and… | Number Work - Even and odd numbers, prime and composite numbers, twin prime, co-prime numbers, triangular and square numbers – Math

Q: A number multiplied by 4 gives 64. That number is square and even. What is that number?

16. 64 ÷ 4 = 1616 = 4² and is an even number.

Math

Number Work - Even and odd numbers, prime and composite numbers, twin prime, co-prime numbers, triangular and square numbers

MCQ

Introduction

Mathematics is built upon different types of numbers. Each type has specific properties related to their factors, divisibility, and patterns. This guide provides an organized look at these classifications using detailed tables.

Detailed Classification of Number Types

1. Even and Odd Numbers

These numbers are determined by their divisibility by 2.

Number Type	Definition	Identification (Units Place)	Examples
Even Numbers	Exactly divisible by 2.	0, 2, 4, 6, 8	24, 50, 72, 100
Odd Numbers	Not exactly divisible by 2.	1, 3, 5, 7, 9	11, 35, 67, 89

2. Prime and Composite Numbers

These are classified based on the number of factors they possess.

Number Type	Definition	Number of Factors	Examples
Prime Numbers	Divisible only by 1 and itself.	Exactly 2 factors	2, 3, 5, 7, 11, 13
Composite Numbers	Has factors other than 1 and itself.	More than 2 factors	4, 6, 8, 9, 10, 12

1 is a unique number; it is neither prime nor composite. 2 is the only even prime number.

3. Twin Prime and Co-prime Numbers

These relate to pairs of numbers and their specific relationships.

Term	Definition	Critical Condition	Examples
Twin Primes	A pair of prime numbers with a difference of 2.	Both numbers must be prime.	(5, 7), (11, 13), (29, 31)
Co-primes	Two numbers with only 1 as a common factor.	No need for the numbers to be prime.	(8, 9), (14, 15), (20, 21)

4. Triangular and Square Numbers

Numbers associated with geometric dot patterns.

Type	Definition / Formula	Examples
Triangular Numbers	Numbers that can form a triangle. Formula: [n × (n+1)] / 2	1, 3, 6, 10, 15, 21...
Square Numbers	Result of multiplying a number by itself. Formula: n × n	1, 4, 9, 16, 25, 36...

Visual dot patterns for triangular and square numbers

Tricks and Shortcuts

Any two consecutive numbers (like 15 and 16) are always co-prime. To find square numbers quickly, remember the patterns of ending digits: squares never end in 2, 3, 7, or 8.

Common Mistakes

Students often think all prime numbers must be odd. This is wrong because 2 is a prime number and it is even.

Practice Questions

Easy Questions

Identify whether 45 is Even or Odd.
List all prime numbers between 1 and 10.
What is the square of 7?

Medium Questions

Is (17, 19) a twin prime pair? Explain why.
Find the 5th triangular number using the formula.
Explain why 9 is a composite number even though it is odd.

Hard Questions

Find a number smaller than 50 that is both a triangular number and a square number.
If you subtract the smallest prime number from the largest prime number under 20, what is the result?
Show that (12, 13) is a co-prime pair by listing their factors.

Revision Summary

Understanding these number types helps in solving complex problems in fractions and algebra. Remember: Prime = 2 factors, Twin Prime = Prime pair with diff 2, Co-prime = only 1 as common factor.

A number multiplied by 4 gives 64. That number is square and even. What is that number?

Explanation

64 ÷ 4 = 16

16 = 4² and is an even number.

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