Highest Common Factor of 682, 429, 664 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 682, 429, 664 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 682, 429, 664 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 682, 429, 664 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 682, 429, 664 is 1.
HCF(682, 429, 664) = 1
HCF of 682, 429, 664 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 682, 429, 664 is 1.
Highest Common Factor of 682,429,664 is 1
Step 1: Since 682 > 429, we apply the division lemma to 682 and 429, to get
682 = 429 x 1 + 253
Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 253 and 429, to get
429 = 253 x 1 + 176
Step 3: We consider the new divisor 253 and the new remainder 176, and apply the division lemma to get
253 = 176 x 1 + 77
We consider the new divisor 176 and the new remainder 77,and apply the division lemma to get
176 = 77 x 2 + 22
We consider the new divisor 77 and the new remainder 22,and apply the division lemma to get
77 = 22 x 3 + 11
We consider the new divisor 22 and the new remainder 11,and apply the division lemma to get
22 = 11 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 682 and 429 is 11
Notice that 11 = HCF(22,11) = HCF(77,22) = HCF(176,77) = HCF(253,176) = HCF(429,253) = HCF(682,429) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 664 > 11, we apply the division lemma to 664 and 11, to get
664 = 11 x 60 + 4
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 4 and 11, to get
11 = 4 x 2 + 3
Step 3: We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 664 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(664,11) .
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Frequently Asked Questions on HCF of 682, 429, 664 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 682, 429, 664?
Answer: HCF of 682, 429, 664 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 682, 429, 664 using Euclid's Algorithm?
Answer: For arbitrary numbers 682, 429, 664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.