Question

Find the H.C.F. of numbers 44 and 99.

Answer 1

Hint: To find the highest common factor (H.C.F) of 44 and 99, we find common prime factors of both the numbers. If there are more than one common factors, we multiply all of them. If there are no common factors, the H.C.F. will be 1.

Complete step by step answer:
 First, list the prime factors of both the numbers.
Prime factors of 44 are:
     \[44=2\times 2\times 11\]
Prime factors of 99 are:
     \[99=3\times 3\times 11\]
Here, the common factor of both the numbers is 11.

Hence, H.C.F of 44 and 99 is 11.

Note: In the above solution, it is necessary that the listed factors are prime numbers. Prime numbers are those numbers that are divided only by 1 and itself.
1) Another way of finding H.C.F of two numbers is through a division method.
In this method, the larger number, 99 in this problem, is divided by the smaller number, 44. If the remainder is not zero, then it becomes the divisor and the last divisor becomes the dividend. This continues until the remainder becomes 0.
The divisor at the very last step becomes the H.C.F of the two numbers.
2) One other way of finding H.C.F. is to list all the factors of both the number and find the highest number which is common among the two. For example: The factors of 44 are 1, 2, 4,11,22 and 44. The factors of 99 are 1,3,9,11,33 and 99. The common factors are 1 and 11. The highest among the two is 11, which makes the H.C.F.