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 1710, 2077 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1710, 2077 is 1 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 1710, 2077 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 1710, 2077 is 1.
HCF(1710, 2077) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1710, 2077 is 1.
Step 1: Since 2077 > 1710, we apply the division lemma to 2077 and 1710, to get
2077 = 1710 x 1 + 367
Step 2: Since the reminder 1710 ≠ 0, we apply division lemma to 367 and 1710, to get
1710 = 367 x 4 + 242
Step 3: We consider the new divisor 367 and the new remainder 242, and apply the division lemma to get
367 = 242 x 1 + 125
We consider the new divisor 242 and the new remainder 125,and apply the division lemma to get
242 = 125 x 1 + 117
We consider the new divisor 125 and the new remainder 117,and apply the division lemma to get
125 = 117 x 1 + 8
We consider the new divisor 117 and the new remainder 8,and apply the division lemma to get
117 = 8 x 14 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1710 and 2077 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(117,8) = HCF(125,117) = HCF(242,125) = HCF(367,242) = HCF(1710,367) = HCF(2077,1710) .
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 1710, 2077?
Answer: HCF of 1710, 2077 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1710, 2077 using Euclid's Algorithm?
Answer: For arbitrary numbers 1710, 2077 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.