Highest Common Factor of 122, 689, 912 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 122, 689, 912 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 122, 689, 912 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 122, 689, 912 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 122, 689, 912 is 1.
HCF(122, 689, 912) = 1
HCF of 122, 689, 912 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 122, 689, 912 is 1.
Highest Common Factor of 122,689,912 is 1
Step 1: Since 689 > 122, we apply the division lemma to 689 and 122, to get
689 = 122 x 5 + 79
Step 2: Since the reminder 122 ≠ 0, we apply division lemma to 79 and 122, to get
122 = 79 x 1 + 43
Step 3: We consider the new divisor 79 and the new remainder 43, and apply the division lemma to get
79 = 43 x 1 + 36
We consider the new divisor 43 and the new remainder 36,and apply the division lemma to get
43 = 36 x 1 + 7
We consider the new divisor 36 and the new remainder 7,and apply the division lemma to get
36 = 7 x 5 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 122 and 689 is 1
Notice that 1 = HCF(7,1) = HCF(36,7) = HCF(43,36) = HCF(79,43) = HCF(122,79) = HCF(689,122) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 912 > 1, we apply the division lemma to 912 and 1, to get
912 = 1 x 912 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 912 is 1
Notice that 1 = HCF(912,1) .
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Frequently Asked Questions on HCF of 122, 689, 912 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 122, 689, 912?
Answer: HCF of 122, 689, 912 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 122, 689, 912 using Euclid's Algorithm?
Answer: For arbitrary numbers 122, 689, 912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.