Highest Common Factor of 274, 689 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 274, 689 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 274, 689 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 274, 689 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 274, 689 is 1.
HCF(274, 689) = 1
HCF of 274, 689 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 274, 689 is 1.
Highest Common Factor of 274,689 is 1
Step 1: Since 689 > 274, we apply the division lemma to 689 and 274, to get
689 = 274 x 2 + 141
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 141 and 274, to get
274 = 141 x 1 + 133
Step 3: We consider the new divisor 141 and the new remainder 133, and apply the division lemma to get
141 = 133 x 1 + 8
We consider the new divisor 133 and the new remainder 8,and apply the division lemma to get
133 = 8 x 16 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 274 and 689 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(133,8) = HCF(141,133) = HCF(274,141) = HCF(689,274) .
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Frequently Asked Questions on HCF of 274, 689 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 274, 689?
Answer: HCF of 274, 689 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 274, 689 using Euclid's Algorithm?
Answer: For arbitrary numbers 274, 689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.