Highest Common Factor of 4075, 1706 using Euclid's algorithm
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 4075, 1706 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 4075, 1706 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 4075, 1706 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 4075, 1706 is 1.
HCF(4075, 1706) = 1
HCF of 4075, 1706 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4075, 1706 is 1.
Highest Common Factor of 4075,1706 is 1
Step 1: Since 4075 > 1706, we apply the division lemma to 4075 and 1706, to get
4075 = 1706 x 2 + 663
Step 2: Since the reminder 1706 ≠ 0, we apply division lemma to 663 and 1706, to get
1706 = 663 x 2 + 380
Step 3: We consider the new divisor 663 and the new remainder 380, and apply the division lemma to get
663 = 380 x 1 + 283
We consider the new divisor 380 and the new remainder 283,and apply the division lemma to get
380 = 283 x 1 + 97
We consider the new divisor 283 and the new remainder 97,and apply the division lemma to get
283 = 97 x 2 + 89
We consider the new divisor 97 and the new remainder 89,and apply the division lemma to get
97 = 89 x 1 + 8
We consider the new divisor 89 and the new remainder 8,and apply the division lemma to get
89 = 8 x 11 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4075 and 1706 is 1
Notice that 1 = HCF(8,1) = HCF(89,8) = HCF(97,89) = HCF(283,97) = HCF(380,283) = HCF(663,380) = HCF(1706,663) = HCF(4075,1706) .
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Frequently Asked Questions on HCF of 4075, 1706 using Euclid's Algorithm
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 4075, 1706?
Answer: HCF of 4075, 1706 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4075, 1706 using Euclid's Algorithm?
Answer: For arbitrary numbers 4075, 1706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.