Question

Use the prime factorization method to determine the HCF of 520 and 1430.

Answer 1

Hint: Using a prime factorization method to solve for the factors for the given numbers need to do factorization and then by seeing the highest common factors of the two numbers given we can finally reach the required solution for our question. Prime factorization methods need to solve for the lowest to the highest possible factors for a given number.

Complete step by step solution:
The given question need to solve for the highest common factors of te given two numbers that is “520” and “1430”, on solving we have to first factorize the given two numbers, on solving we get:
\[
   \Rightarrow 520 = 1 \times 2 \times 2 \times 2 \times 5 \times 13 \\
   \Rightarrow 1430 = 1 \times 2 \times 5 \times 13 \times 13 \\
 \]
Here we have factorize the given two numbers and now we need to solve for the highest common factors for the numbers, for which we need to first get the common factors and then out of those common factors we have to decide for the highest common factor, on solving we get:
\[ \Rightarrow common\,factors\,are\,:\,1,2,5,13\]
Hence highest common factor is the product of these factors, on solving we get:
\[ \Rightarrow H.C.F = 1 \times 2 \times 5 \times 13 = 130\]

Hence highest common factor for the given two numbers, on solving we get as “130”, which is the final solution for the question.

Note: The given question needs to find the highest common factor for the given two numbers, and we need to solve it by prime factorization only. Here once you have the highest common factor then we can check for the solution by dividing the number by the obtained solution and we will get a perfect divisor with zero remainder.