Highest Common Factor of 124, 689, 680 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 124, 689, 680 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 124, 689, 680 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 124, 689, 680 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 124, 689, 680 is 1.
HCF(124, 689, 680) = 1
HCF of 124, 689, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 124, 689, 680 is 1.
Highest Common Factor of 124,689,680 is 1
Step 1: Since 689 > 124, we apply the division lemma to 689 and 124, to get
689 = 124 x 5 + 69
Step 2: Since the reminder 124 ≠ 0, we apply division lemma to 69 and 124, to get
124 = 69 x 1 + 55
Step 3: We consider the new divisor 69 and the new remainder 55, and apply the division lemma to get
69 = 55 x 1 + 14
We consider the new divisor 55 and the new remainder 14,and apply the division lemma to get
55 = 14 x 3 + 13
We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get
14 = 13 x 1 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 124 and 689 is 1
Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(55,14) = HCF(69,55) = HCF(124,69) = HCF(689,124) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 1, we apply the division lemma to 680 and 1, to get
680 = 1 x 680 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 680 is 1
Notice that 1 = HCF(680,1) .
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Frequently Asked Questions on HCF of 124, 689, 680 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 124, 689, 680?
Answer: HCF of 124, 689, 680 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 124, 689, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 124, 689, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.