Highest Common Factor of 689, 41576 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, 41576 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 689, 41576 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, 41576 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, 41576 is 1.
HCF(689, 41576) = 1
HCF of 689, 41576 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, 41576 is 1.
Highest Common Factor of 689,41576 is 1
Step 1: Since 41576 > 689, we apply the division lemma to 41576 and 689, to get
41576 = 689 x 60 + 236
Step 2: Since the reminder 689 ≠ 0, we apply division lemma to 236 and 689, to get
689 = 236 x 2 + 217
Step 3: We consider the new divisor 236 and the new remainder 217, and apply the division lemma to get
236 = 217 x 1 + 19
We consider the new divisor 217 and the new remainder 19,and apply the division lemma to get
217 = 19 x 11 + 8
We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get
19 = 8 x 2 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 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 689 and 41576 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(217,19) = HCF(236,217) = HCF(689,236) = HCF(41576,689) .
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Frequently Asked Questions on HCF of 689, 41576 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, 41576?
Answer: HCF of 689, 41576 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 689, 41576 using Euclid's Algorithm?
Answer: For arbitrary numbers 689, 41576 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
