Test: Number, Square Numbers - Year 5 MCQ

A prime number has exactly two distinct positive divisors: 1 and itself. The number 17 meets this criterion since its only divisors are 1 and 17. Recognizing prime numbers is crucial in number theory and has applications in cryptography.

A square number is a number that can be made by multiplying a whole number by itself.

• 25 is a square number because it equals 5 × 5.
• The other numbers cannot be made by multiplying a whole number by itself.

So, 25 is the correct answer.

The Sieve of Eratosthenes is an ancient algorithm used to identify all prime numbers up to a specified integer. By systematically crossing out the multiples of each prime starting from 2, the remaining numbers are primes. This efficient method highlights how primes can be found without direct division.

The 4th triangular number is calculated by adding the first four natural numbers together. Here’s how it works:

• 1st number: 1
• 2nd number: 2
• 3rd number: 3
• 4th number: 4

Now, add them up:

• 1 + 2 + 3 + 4 = 10

Thus, the 4th triangular number is 10.

To find out if a number is divisible by 4, follow these steps:

• Look at the last two digits of the number.
• If these two digits form a number that is divisible by 4, then the entire number is also divisible by 4.

For example:

• The number 124: Last two digits are 24, which is divisible by 4.
• The number 153: Last two digits are 53, which is not divisible by 4.

This method is quick and reliable for checking divisibility by 4.

When you multiply 5 by itself, you find the answer by calculating:

• 5 times 5 equals 25.

So, the result is 25.

The factor pair (3, 3) means we are looking for a number that can be expressed as the product of 3 and 3. This product is:

• 3 × 3 = 9

Thus, the number with the factor pair (3, 3) is 9.

The first five odd numbers are 1, 3, 5, 7, and 9. Their sum is 1 + 3 + 5 + 7 + 9 = 25, which is also 5², illustrating that the sum of the first n odd numbers equals n². This property connects arithmetic and algebra beautifully.

The number 36 is both a square number (6 × 6) and a triangular number (1 + 2 + 3 + 4 + 5 + 6). This duality illustrates the fascinating connections between different sets of numbers in mathematics, showing that some numbers can belong to multiple categories.

A number is divisible by 2 if its ones digit is even, which includes the digits 0, 2, 4, 6, and 8. This simple rule helps quickly determine divisibility without performing long division, making it a handy tool in arithmetic.

A square number is defined as a number that results from multiplying a number by itself. For example, 3 × 3 = 9 and 4 × 4 = 16. This concept is foundational in mathematics, as square numbers appear in various areas, including geometry and algebra. Interestingly, square numbers can also be visually represented as grids of smaller squares, illustrating their geometric nature.

The sequence of triangular numbers begins with 1, 3, 6, 10, and 15, where each number is the sum of consecutive natural numbers. For example, 1 = 1, 3 = 1 + 2, 6 = 1 + 2 + 3, and so forth. Triangular numbers can be visualized as dots arranged in a triangle, which shows their unique geometric properties.

A number is divisible by 4 if the last two digits of that number form a number that is divisible by 4. For example, in the number 1,736, the last two digits are 36, and since 36 ÷ 4 = 9, the number is indeed divisible by 4. This rule simplifies the process of checking divisibility without performing full division.

A prime number is defined as a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For instance, the number 7 is prime because its only divisors are 1 and 7. Interestingly, the number 2 is the only even prime number, highlighting that all other even numbers can be divided by 2, thus having more than two divisors.

The Sieve of Eratosthenes is an efficient algorithm used to identify all prime numbers up to a given limit, typically 100. It works by iteratively marking the multiples of each prime number starting from 2, thus eliminating non-prime numbers. This method not only highlights the beauty of number theory but also serves as a foundational technique in computational mathematics for generating lists of primes efficiently.