Question

What is the greatest number by which 1037 and 1159 can both be divided exactly?

Answer 1

Hint: Find the HCF of 1037 and 1159 because HCF will give us the number which is a factor of both the numbers and also the common factor and highest of all.

Complete step-by-step answer:
We had to find HCF of 1037 and 1159.
To find HCF of two numbers we perform division till we get the remainder equal to zero.
And the last divisor that we get will be the HCF of two given numbers

So, the steps of the above long division is explained below.
First, the divisor will be the smallest number and dividend will be the other number.
So, 1037 = divisor
And 1159 = dividend
So, performing division. We get,
1159 = 1037*1 + 122
Remainder = 122 and Quotient = 1
Now, divisor(1037) will become the dividend and remainder(122) will become the divisor.
So, performing division. We get,
1037 = 122*8 + 61
Remainder = 61 and Quotient = 8
Now, divisor(122) will become the dividend and remainder(61) will become the divisor.
So, performing division. We get,
122 = 61*2 + 0
Remainder = 0 and Quotient = 2
As, we know that if we get remainder equal to zero then the divisor will be HCF of the given two numbers.
So, divisor = 61
HCF of 1037 and 1159 will be 61.
Hence, 61 will be the greatest number by which 1037 and 1159 can both be divided exactly.


Note: Whenever we come up with this type of problem then the easiest and efficient way to find the solution of the problem is by calculating HCF of the given numbers. And we can also find the HCF of the given numbers by other methods, and that is first, find the set of all the factors of both numbers and then find that factor that is common to both the sets of factors. After that multiply all common factors to get the HCF and required answer of the problem.