分步说明
Gather Your Inputs
First, identify the number you want to find the prime factorisation of. This number should be a positive integer. For example, let's say we want to find the prime factorisation of 315.
Find the Smallest Prime Factor
Next, find the smallest prime number that divides the given number exactly. The smallest prime number is 2. If the number is divisible by 2, divide it by 2 and write it down as a factor. If it's not divisible by 2, move on to the next prime number, which is 3. Continue this process until you find a prime factor. For example, 315 is not divisible by 2, but it is divisible by 3, so we write 3 as a factor and divide 315 by 3 to get 105.
Continue Dividing by Prime Factors
Continue dividing the quotient by prime numbers until you can't divide anymore. For example, 105 is divisible by 3, so we divide it by 3 to get 35. Then, 35 is divisible by 5, so we divide it by 5 to get 7. Since 7 is a prime number, we can't divide anymore, so we stop here. The prime factorisation of 315 is 3 x 3 x 5 x 7, or $3^2 * 5 * 7$ in exponent notation.
Write the Prime Factorisation in Exponent Notation
Finally, write the prime factorisation in exponent notation. This involves grouping the same prime factors together and raising them to the power of the number of times they appear. For example, the prime factorisation of 315 is $3^2 * 5 * 7$. This shows that the prime factors of 315 are 3, 5, and 7, and that 3 appears twice.
Check Your Work
To check your work, multiply the prime factors together to make sure you get the original number. For example, $3^2 * 5 * 7 = 9 * 5 * 7 = 45 * 7 = 315$. This confirms that the prime factorisation is correct.
Using a Calculator for Convenience
While it's possible to find the prime factorisation of a number by hand, it can be time-consuming for large numbers. In these cases, it's often more convenient to use a calculator or computer program to find the prime factorisation. Many calculators and computer programs have built-in functions for finding prime factorisations, which can save time and reduce the risk of error.
Introduction to Prime Factorisation
Prime factorisation is the process of finding the prime factors of a given integer. A prime factor is a prime number that divides the given integer exactly. The prime factorisation of a number can be expressed in exponent notation, which shows the prime factors and their powers.
What is Prime Factorisation?
Prime factorisation is a way of expressing a number as a product of its prime factors. This can be useful in a variety of mathematical contexts, such as solving equations, finding the greatest common divisor, and simplifying fractions.
Step-by-Step Guide to Prime Factorisation
To calculate the prime factorisation of a number, follow these steps: