Sir Shib Math Page

19/02/2024

Answer to a question by a viewer Onalenna Ramogale

12/02/2024

Hi everyone! Today I want to share with you a simple way to find the greatest common factor (GCF) of two numbers using the listing method. The GCF of two numbers is the largest number that can divide both of them without leaving any remainder. For example, the GCF of 12 and 18 is 6, because 6 is the largest number that can divide both and 18 evenly.

So how do we find the GCF using the listing method? It’s very easy. Just follow these three steps:

1. List all the factors of each number. Factors are the numbers that can divide a number evenly.

2. Identify the common factors of both numbers. Common factors are the factors that both numbers have in common.

3. Choose the largest common factor. This is the GCF of the two numbers.

That’s it! You have found the GCF using the listing method. You can use this method for any pair of numbers. Just remember to list all the factors, identify the common factors, and choose the largest one. I hope this post was helpful to you. If you have any questions or comments, feel free to leave them below. Thanks for watching! 😊

25/01/2024

Prime factors are the prime numbers that divide a given number exactly. Continuous division is a method of finding the prime factors of a number by repeatedly dividing it by the smallest possible prime factor. Here are the steps to follow:

• Write down the number you want to factorize.

• Divide it by the smallest prime number that divides it evenly. Write the quotient below the dividend.

• Repeat this process with the quotient, until you reach 1 or a prime number as the final quotient.

• The prime factors are the divisors you used in each step. You can write them as a product using multiplication signs.

For example, let’s find the prime factors of 60 using continuous division.

• Write 60 as the dividend.

• Divide it by 2, the smallest prime number that divides it evenly. Write 30 as the quotient below 60.

• Divide 30 by 2 again, and write 15 as the quotient below 30.

• Divide 15 by 3, the smallest prime number that divides it evenly. Write 5 as the quotient below 15.

• Divide 5 by 5, and write 1 as the quotient below 5.

• The final quotient is 1, so we stop the process.

• The prime factors are 2, 2, 3, and 5. We can write them as a product:

60=2×2×3×5

I hope this explanation helps you understand how to find prime factors using continuous division. 😊

23/01/2024

Prime factorization is the process of finding which prime numbers multiply together to make a given number. A prime number is a whole number that can only be divided by 1 and itself, such as 2, 3, 5, 7, etc. A factor tree is a diagram that shows how to break down a number into its prime factors.

To use a factor tree, you start with the number you want to factorize and then divide it by any factor of that number. You write the two factors below the original number and connect them with branches. Then you repeat the process for each factor until you reach only prime numbers. The prime numbers at the bottom of the tree are the prime factors of the original number.

If you want to learn more about prime factorization and factor trees, you can watch my video I hope this helps you understand the concept better. 😊

23/01/2024

22/01/2024

What are Prime and Composite Numbers?

In mathematics, we often encounter different types of numbers, such as natural numbers, integers, rational numbers, irrational numbers, and so on. But among these numbers, there is a special category of numbers that have a unique property: they are called prime numbers.

A prime number is a natural number that has exactly two positive factors: 1 and itself. For example, 2 is a prime number because it has only two factors: 1 and 2. Similarly, 3, 5, 7, 11, 13, 17, and so on are prime numbers.

On the other hand, a composite number is a natural number that has more than two positive factors. For example, 4 is a composite number because it has four factors: 1, 2, 4, and itself. Similarly, 6, 8, 9, 10, 12, 14, and so on are composite numbers.

One way to check whether a number is prime or composite is to try dividing it by all the natural numbers from 2 to its square root. If the number is divisible by any of these numbers, then it is composite. Otherwise, it is prime. For example, to check whether 17 is prime or composite, we can try dividing it by 2, 3, 4, and 5. Since none of these numbers divide 17, we can conclude that 17 is prime.

However, this method can be very tedious and time-consuming, especially for large numbers. Is there a faster and easier way to find all the prime numbers up to a certain limit? Yes, there is. It is called the sieve of Eratosthenes.

How to Find the Prime Numbers Using the Sieve of Eratosthenes?

The sieve of Eratosthenes is an ancient algorithm that was invented by a Greek mathematician named Eratosthenes in the third century BC. It is one of the most efficient ways to find all the prime numbers smaller than a given number n. Here are the steps to follow the sieve of Eratosthenes:

• Step 1: Write down all the natural numbers from 2 to n in a list or a table.

• Step 2: Cross out 1, as it is neither prime nor composite.

• Step 3: Circle the first number in the list that is not crossed out. This number is prime. Let’s call it p.

• Step 4: Cross out all the multiples of p in the list, starting from p^2. These numbers are composite.

• Step 5: Repeat steps 3 and 4 until you reach the square root of n. All the numbers that are not crossed out at this point are prime.