Question

Find the HCF by finding factors: 75, 79, 89.
(a) 2
(b) 3
(c) 1
(d) 4

Answer 1

Hint: First, we will understand the concept of Highest common factor (HCF) which is given as the greatest number which can divide the given numbers. Then using this concept, we will find the factors of 75, 79, 89 and then we will see in all the three factors which is the common factor that will be our answer.

Complete step-by-step answer:
Here, we will first understand the concept of HCF.
Highest Common factor (HCF) is the greatest number which can divide the given numbers. It is also called as Greatest common Divisor (GCD). For example: if we take two numbers i.e. 4, 6 then factors of these both will be \[4=2\times 2\] , \[6=2\times 3\] . Now, we can see that in both factors only 2 are common, so HCF will be 2.
Using the same concept, we will first find factors of 75, 79, 89. So, we will get as
\[75=5\times 5\times 3\times 1\]
\[79=1\times 79\]
\[89=1\times 89\]
We can see that there are no common factors in all the three numbers except 1, so, HF will be 1.
Thus, HCF of 75, 79, 89 is 1.
So, the correct answer is “Option c”.

Note: Do not get confused between Least common multiple and highest common factor. If instead of HCF, LCM is taken the answer will be wrong. After finding factor i.e. \[75=5\times 5\times 3\times 1\] , \[79=1\times 79\] , \[89=1\times 89\] LCM will be \[5\times 5\times 3\times 79\times 89\times 1=527325\] . So, be careful about what is asked in question and then solve it. We can easily eliminate the options and find the answer. The numbers given are all odd numbers, which means they will not be divisible by 2. Also, they will not be divisible by 4 as the last digit of the numbers are not 0, 2, 4, 6 or 8. So, 2 and 4 cannot be factors. Now the sum of digits must be divisible by 3 for 3 to be a factor, so 7+5=12, 7+9=16, 8+9=17. We can see that only 75 is divisible by 3, but we are asked for HCF, the highest common factor. So, 3 cannot be the answer. Hence 1 is the correct answer.