Find the HCF 1836,810,1296 and 702.

Hint: HCF of the numbers is the greatest integer, which will divide numbers exactly. HCF is
elaborated as the Highest Common Factor. To find the HCF of the given numbers, find the prime factors
of each number and multiply the entire unique (single) prime factors to get the result. The prime factor
of the number is the prime number when multiplied together, will give the original number.
There are two methods to factorize a number one by division method, where the number is divided by
the prime number to get the smallest number. Another method is the factor tree, where the number is
broken down into factors to get the smallest number. Here, the question is asking for the HCF of the
numbers 1836, 810, 1296, and 702 so, the first step will be to factorize the numbers and then multiply
the common unique numbers among the factors of all numbers. The factors are the integers, which,
when multiplied, results in the number itself.

Complete step by step solution:
To determine the HCF of the given numbers, first find their factors:
\[
1836 = 2 \times 2 \times 3 \times 3 \times 3 \times 17 \\
810 = 2 \times 3 \times 3 \times 3 \times 3 \times 5 \\
1296 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \\
702 = 2 \times 3 \times 3 \times 3 \times 13 \\
\]
Now, find the common unique factors and then find the HCF.
\[
HCF\left( {1836,810,1296,702} \right) = 2 \times 3 \times 3 \times 3 \\
= 54 \\
\]
Hence, the HCF of the given numbers 1836, 810, 1296, and 702 is 54.
Note: HCF of a number can also be found by the division method. The highest common factor or the
greatest common factor of two or more numbers is the greatest number which divides exactly the given
number.