Highest Common Factor of 770, 2095 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 770, 2095 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 770, 2095 is 5 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 770, 2095 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 770, 2095 is 5.
HCF(770, 2095) = 5
HCF of 770, 2095 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 770, 2095 is 5.
Highest Common Factor of 770,2095 is 5
Step 1: Since 2095 > 770, we apply the division lemma to 2095 and 770, to get
2095 = 770 x 2 + 555
Step 2: Since the reminder 770 ≠ 0, we apply division lemma to 555 and 770, to get
770 = 555 x 1 + 215
Step 3: We consider the new divisor 555 and the new remainder 215, and apply the division lemma to get
555 = 215 x 2 + 125
We consider the new divisor 215 and the new remainder 125,and apply the division lemma to get
215 = 125 x 1 + 90
We consider the new divisor 125 and the new remainder 90,and apply the division lemma to get
125 = 90 x 1 + 35
We consider the new divisor 90 and the new remainder 35,and apply the division lemma to get
90 = 35 x 2 + 20
We consider the new divisor 35 and the new remainder 20,and apply the division lemma to get
35 = 20 x 1 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 770 and 2095 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(35,20) = HCF(90,35) = HCF(125,90) = HCF(215,125) = HCF(555,215) = HCF(770,555) = HCF(2095,770) .
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Frequently Asked Questions on HCF of 770, 2095 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 770, 2095?
Answer: HCF of 770, 2095 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 770, 2095 using Euclid's Algorithm?
Answer: For arbitrary numbers 770, 2095 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.