Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 5740, 1660 i.e. 20 the largest integer that leaves a remainder zero for all numbers.
HCF of 5740, 1660 is 20 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 5740, 1660 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 5740, 1660 is 20.
HCF(5740, 1660) = 20
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5740, 1660 is 20.
Step 1: Since 5740 > 1660, we apply the division lemma to 5740 and 1660, to get
5740 = 1660 x 3 + 760
Step 2: Since the reminder 1660 ≠ 0, we apply division lemma to 760 and 1660, to get
1660 = 760 x 2 + 140
Step 3: We consider the new divisor 760 and the new remainder 140, and apply the division lemma to get
760 = 140 x 5 + 60
We consider the new divisor 140 and the new remainder 60,and apply the division lemma to get
140 = 60 x 2 + 20
We consider the new divisor 60 and the new remainder 20,and apply the division lemma to get
60 = 20 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 5740 and 1660 is 20
Notice that 20 = HCF(60,20) = HCF(140,60) = HCF(760,140) = HCF(1660,760) = HCF(5740,1660) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 5740, 1660?
Answer: HCF of 5740, 1660 is 20 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5740, 1660 using Euclid's Algorithm?
Answer: For arbitrary numbers 5740, 1660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.