Highest Common Factor of 685, 502, 777 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 685, 502, 777 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 685, 502, 777 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 685, 502, 777 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 685, 502, 777 is 1.
HCF(685, 502, 777) = 1
HCF of 685, 502, 777 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 685, 502, 777 is 1.
Highest Common Factor of 685,502,777 is 1
Step 1: Since 685 > 502, we apply the division lemma to 685 and 502, to get
685 = 502 x 1 + 183
Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 183 and 502, to get
502 = 183 x 2 + 136
Step 3: We consider the new divisor 183 and the new remainder 136, and apply the division lemma to get
183 = 136 x 1 + 47
We consider the new divisor 136 and the new remainder 47,and apply the division lemma to get
136 = 47 x 2 + 42
We consider the new divisor 47 and the new remainder 42,and apply the division lemma to get
47 = 42 x 1 + 5
We consider the new divisor 42 and the new remainder 5,and apply the division lemma to get
42 = 5 x 8 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 685 and 502 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(42,5) = HCF(47,42) = HCF(136,47) = HCF(183,136) = HCF(502,183) = HCF(685,502) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 777 > 1, we apply the division lemma to 777 and 1, to get
777 = 1 x 777 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 777 is 1
Notice that 1 = HCF(777,1) .
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Frequently Asked Questions on HCF of 685, 502, 777 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 685, 502, 777?
Answer: HCF of 685, 502, 777 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 685, 502, 777 using Euclid's Algorithm?
Answer: For arbitrary numbers 685, 502, 777 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
