Question - Finding Highest Common Factor Using Prime Factorization Method
Solution:
The image shows a mathematical problem asking to find the Highest Common Factor (HCF) or Greatest Common Divisor (GCD) of given number sets using the prime factorization method. Specifically, the problem (b) listed is to find the HCF of (32, 16). Let's solve this problem by finding the prime factorization of each number.Prime factorization of 32:32 = 2 x 2 x 2 x 2 x 2Or we can write this as 32 = 2^5 (since there are five 2's multiplied together).Prime factorization of 16:16 = 2 x 2 x 2 x 2Or we can write this as 16 = 2^4 (since there are four 2's multiplied together).To find the HCF, we take the lowest power of common prime factors. Here we have the prime number 2 as the common factor in both numbers.The lowest power of 2 that is common in both 32 and 16 is 2^4. Hence, the HCF of 32 and 16 is 2^4 which is 16.Therefore, the HCF (or GCD) of (32, 16) is 16.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com