Prime factors
A number that only has two factors - itself and one. factors are A factor is a number which divides exactly into another number. 1 is a factor of every number and every number is a factor of itself. A number can have several factors. Example: 1, 2, 5 and 10 are the factors of 10. of a number that are, themselves, prime numbers.
There are many methods to find the prime factors of a number, but one of the most common is to use a prime factor tree.
Example
Write 40 as the To multiply. The product of two numbers is the answer to the multiplication of the numbers. The product of 5 and 8 is 40. of its prime factors.
Firstly, find two numbers that will multiply together to give 40. These are factors of 40. \(4 \times 10 = 40\) would be one way of doing this calculation. Every integer has a unique prime factorisation, so it doesn鈥檛 matter which factors are chosen to start the factor tree.
Neither 4 nor 10 is a prime number, and this question is looking for prime factors, so each number must be broken down again into Pairs of factors multiplied together to get a certain product.. Continue breaking down the factors into factor pairs until you are only left with prime numbers. Then circle these prime numbers.
The question has asked for a product of prime factors. Write all of the circled prime numbers (found in the prime factor tree) as a product.
This gives \(2 \times 2 \times 2 \times 5\). This can be written in index form as \(2^3 \times 5\)
This answer can be checked by making sure \(2 \times 2 \times 2 \times 5\) is equal to 40. \(2 \times 2 \times 2 \times 5 = 40\), so this answer is correct. The final answer is \(2^3 \times 5\).
Question
Express 24 as a product of prime factors.
Here is one way to break down 24 into prime factors:
Now write 24 as a product of the circled prime numbers, \(2 \times 2 \times 2 \times 3 = 2^3 \times 3\). As a check, work out \(2 \times 2 \times 2 \times 3\) to make sure it gives an answer of 24.