Number Theory

To find the Highest Common Factor (HCF) of 48 and 96, we can observe that 96 is a multiple of 48 (96 = 48 * 2).

When one number is a multiple of another, the smaller number is the HCF.

Therefore, the HCF of 48 and 96 is 48.

The factors of 4800 are the numbers that divide evenly into 4800. Here's a list of all the factors:

• 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 150, 160, 192, 200, 240, 300, 320, 400, 480, 600, 800, 960, 1200, 1600, 2400, 4800

These are all the positive integers that divide 4800 without leaving a remainder.

Let's identify the prime numbers between 90 and 100. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

• 91 = 7 x 13
• 92 = 2 x 46
• 93 = 3 x 31
• 94 = 2 x 47
• 95 = 5 x 19
• 96 = 2 x 48
• 97 = Prime
• 98 = 2 x 49
• 99 = 3 x 33

Therefore, the only prime number between 90 and 100 is 97.

So, there is only 1 prime number between 90 and 100.

Here's the breakdown of divisibility for the numbers 2 and 4:

• 2:
  • The number 2 is a prime number.
  • Prime numbers are only divisible by 1 and themselves.
  • Therefore, 2 is only divisible by 1 and 2.
• 4:
  • The number 4 is not a prime number.
  • The factors of 4 are 1, 2, and 4.
  • Therefore, 4 is divisible by 1, 2, and 4.

Here are three rational numbers between -1 and -2:

• -1.25 which can be expressed as the fraction -5/4
• -1.5 which can be expressed as the fraction -3/2
• -1.75 which can be expressed as the fraction -7/4

A rational number is any number that can be expressed as a fraction where both the numerator and denominator are integers. Because there are an infinite amount of numbers between any two numbers, there are also an infinite amount of rational numbers between -1 and -2.

Numbers of the form a + bi , where a and b are real numbers and i is the imaginary unit (defined as the square root of -1), are called complex numbers .