10 (a) Show that 95 is not a prime number - OCR - GCSE Maths - Question 10 - 2023 - Paper 6

To find the HCF, we first identify the prime factors of the numbers:

• The prime factorization of 2000 is given as: $2000 = 2^2 × 5^3$
• The prime factorization of 8750 is given as: $8750 = 2^1 × 5^5 × 7$

Next, we take the lowest power of each common prime factor:

• For the prime factor 2: the minimum power is $ext{min}(2, 1) = 1$
• For the prime factor 5: the minimum power is $ext{min}(3, 5) = 3$

Thus, the HCF is given by:

$HCF = 2^{ ext{min}(2, 1)} × 5^{ ext{min}(3, 5)} = 2^1 × 5^3 = 2 × 125 = 250$

First, we will factorize 10:

$10 = 2 × 5$

Thus, we can write:

$2 × 10^{12} = 2 × (2 × 5)^{12}$

This expands to:

$2 × 2^{12} × 5^{12} = 2^{1 + 12} × 5^{12} = 2^{13} × 5^{12}$

So, the final prime factorization is:

$2^{13} × 5^{12}$