Highest Common Factor of 680, 536, 117, 89 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, 536, 117, 89 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 536, 117, 89 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 680, 536, 117, 89 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, 536, 117, 89 is 1.
HCF(680, 536, 117, 89) = 1
HCF of 680, 536, 117, 89 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, 536, 117, 89 is 1.
Highest Common Factor of 680,536,117,89 is 1
Step 1: Since 680 > 536, we apply the division lemma to 680 and 536, to get
680 = 536 x 1 + 144
Step 2: Since the reminder 536 ≠ 0, we apply division lemma to 144 and 536, to get
536 = 144 x 3 + 104
Step 3: We consider the new divisor 144 and the new remainder 104, and apply the division lemma to get
144 = 104 x 1 + 40
We consider the new divisor 104 and the new remainder 40,and apply the division lemma to get
104 = 40 x 2 + 24
We consider the new divisor 40 and the new remainder 24,and apply the division lemma to get
40 = 24 x 1 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 680 and 536 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(40,24) = HCF(104,40) = HCF(144,104) = HCF(536,144) = HCF(680,536) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 117 > 8, we apply the division lemma to 117 and 8, to get
117 = 8 x 14 + 5
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 5 and 8, to get
8 = 5 x 1 + 3
Step 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 8 and 117 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(117,8) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 89 > 1, we apply the division lemma to 89 and 1, to get
89 = 1 x 89 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 89 is 1
Notice that 1 = HCF(89,1) .
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Frequently Asked Questions on HCF of 680, 536, 117, 89 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, 536, 117, 89?
Answer: HCF of 680, 536, 117, 89 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 536, 117, 89 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 536, 117, 89 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.