Question

find the greatest number that divides 3128 and 420 ​

Answer 1

$\textbf{Given numbers are 3128 and 420}$

$\textbf{To find: GCD of 3128 and 420}$

$\text{We are going to find the GCD by prime factorization method}$

$\begin{array}{r|c}2&3128\\\cline{2-2}2&1564\\\cline{2-2}2&782\\\cline{2-2}17&391\\\cline{2-2}23&23\\\cline{2-2}&1\end{array}$

$\begin{array}{r|c}2&420\\\cline{2-2}2&210\\\cline{2-2}3&105\\\cline{2-2}5&35\\\cline{2-2}7&7\\\cline{2-2}&1\end{array}$

$\text{Now,}$

$3128=2^3{\times}17{\times}23$

$420=2^2{\times}5^2{\times}7$

$\text{Here, 2^2 is the only common factor to both 3128 and 420}$

$\implies\bf\;GCD=4$

$\therefore\textbf{The GCD of 3128 and 420 is 4}$

Find more:

Find the ratio between HCF and LCM of 10 15 and 20

https://brainly.in/question/15064394