Highest Common Factor of 689, 500, 569, 852 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 689, 500, 569, 852 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 689, 500, 569, 852 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 689, 500, 569, 852 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 689, 500, 569, 852 is 1.
HCF(689, 500, 569, 852) = 1
HCF of 689, 500, 569, 852 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 689, 500, 569, 852 is 1.
Highest Common Factor of 689,500,569,852 is 1
Step 1: Since 689 > 500, we apply the division lemma to 689 and 500, to get
689 = 500 x 1 + 189
Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 189 and 500, to get
500 = 189 x 2 + 122
Step 3: We consider the new divisor 189 and the new remainder 122, and apply the division lemma to get
189 = 122 x 1 + 67
We consider the new divisor 122 and the new remainder 67,and apply the division lemma to get
122 = 67 x 1 + 55
We consider the new divisor 67 and the new remainder 55,and apply the division lemma to get
67 = 55 x 1 + 12
We consider the new divisor 55 and the new remainder 12,and apply the division lemma to get
55 = 12 x 4 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 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 689 and 500 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(55,12) = HCF(67,55) = HCF(122,67) = HCF(189,122) = HCF(500,189) = HCF(689,500) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 569 > 1, we apply the division lemma to 569 and 1, to get
569 = 1 x 569 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 569 is 1
Notice that 1 = HCF(569,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 852 > 1, we apply the division lemma to 852 and 1, to get
852 = 1 x 852 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 852 is 1
Notice that 1 = HCF(852,1) .
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Frequently Asked Questions on HCF of 689, 500, 569, 852 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 689, 500, 569, 852?
Answer: HCF of 689, 500, 569, 852 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 689, 500, 569, 852 using Euclid's Algorithm?
Answer: For arbitrary numbers 689, 500, 569, 852 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.