EDEXCEL GCSE FOUNDATION MATHS - What is the Product of Primes

Edexcel GCSE Foundation Maths: Product of Primes

What are prime numbers?

A prime number is a whole number greater than 1 that has only two factors (divisors): 1 and itself.

• Examples of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19...

What is the product of primes?

The product of primes is a way of representing any whole number greater than 1 as a product of prime numbers.

How to find the product of primes:

1. Start with the original number.
2. Find the smallest prime number that divides the number evenly.
3. Divide the number by the prime number.
4. Repeat steps 2 and 3 with the new quotient until you are left with a prime number.

Example: Find the product of primes for 36.

1. Original number: 36
2. Smallest prime factor: 2 (36 ÷ 2 = 18)
3. New quotient: 18
4. Smallest prime factor: 2 (18 ÷ 2 = 9)
5. New quotient: 9
6. Smallest prime factor: 3 (9 ÷ 3 = 3)
7. New quotient: 3 (This is a prime number)

Therefore, the product of primes for 36 is 2 × 2 × 3 × 3, which can be written as 2² × 3².

Key points:

• Every whole number greater than 1 can be written as a product of prime numbers.
• The order of the prime factors does not matter.
• The product of primes is also known as the prime factorization.

Example Questions:

1. Find the product of primes for 42.
2. Express 60 as a product of its prime factors.
3. What is the highest common factor (HCF) of 12 and 18?

Answers:

1. 2 × 3 × 7
2. 2² × 3 × 5
3. 6 (HCF is the product of the common prime factors, raised to their lowest power)

Practice:

Practice finding the product of primes for different numbers. You can use a factor tree to help you visualize the process.

Remember: Understanding the product of primes is a key concept in number theory and will be useful in various areas of mathematics.