Question

870 to 225 HCF is:
A) 15
B) 10
C) 25
D) None of these

Answer 1

Hint:
Here, we will find the factors of the two numbers by using the prime factorization method. Then we will multiply the factors which are common in both the numbers to get the required highest common factor (H.C.F.) of the two numbers.

Complete step by step solution:
We have to find the H.C.F. of two numbers. A Highest common factor (H.C.F.) is the greatest number that is a factor of two or more numbers. This is also known as the Greatest Common Factor (G.C.F.).
By using the prime factorization method, we will find the factor of the given two numbers.
Therefore, prime factorization of 870 is:
$\begin{array}{*{20}{l}}
  2| {870} \\
\hline
  3| {435} \\
\hline
  5| {145} \\
\hline
  {29}| {29} \\
\hline
  {}| 1
\end{array}$
Hence, 870 can be written as:
$870 = 2 \times 3 \times 5 \times 29$
Also, prime factorization of 225 is:
$\begin{array}{*{20}{l}}
  3| {225} \\
\hline
  3| {75} \\
\hline
  5| {25} \\
\hline
  5| 5 \\
\hline
  {}| 1
\end{array}$
Hence, 225 can be written as:
$225 = 3 \times 3 \times 5 \times 5$
In both the numbers, we can find the numbers 3 and 5 multiplying with all the other factors. Hence, $H.C.F\left( {870,225} \right) = 3 \times 5 = 15$.
Therefore, H.C.F. of 870 and 225 is 15.

Hence, option A is the correct answer.

Note:
In order to find HCF of two numbers it is important to express those numbers as a product of their prime factors. Prime factors are those factors that are greater than 1 and have only two factors, i.e. factor 1 and the prime number itself. Now, in order to express the given number as a product of its prime factors, we are required to do the prime factorization of the given number. Factorization is a method of writing an original number as the product of its various factors.