Highest Common Factor of 680, 73156 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 680, 73156 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 73156 is 4 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 680, 73156 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 680, 73156 is 4.
HCF(680, 73156) = 4
HCF of 680, 73156 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 680, 73156 is 4.
Highest Common Factor of 680,73156 is 4
Step 1: Since 73156 > 680, we apply the division lemma to 73156 and 680, to get
73156 = 680 x 107 + 396
Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 396 and 680, to get
680 = 396 x 1 + 284
Step 3: We consider the new divisor 396 and the new remainder 284, and apply the division lemma to get
396 = 284 x 1 + 112
We consider the new divisor 284 and the new remainder 112,and apply the division lemma to get
284 = 112 x 2 + 60
We consider the new divisor 112 and the new remainder 60,and apply the division lemma to get
112 = 60 x 1 + 52
We consider the new divisor 60 and the new remainder 52,and apply the division lemma to get
60 = 52 x 1 + 8
We consider the new divisor 52 and the new remainder 8,and apply the division lemma to get
52 = 8 x 6 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 680 and 73156 is 4
Notice that 4 = HCF(8,4) = HCF(52,8) = HCF(60,52) = HCF(112,60) = HCF(284,112) = HCF(396,284) = HCF(680,396) = HCF(73156,680) .
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Frequently Asked Questions on HCF of 680, 73156 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 680, 73156?
Answer: HCF of 680, 73156 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 73156 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 73156 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.