Highest Common Factor of 712, 908, 268, 371 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 712, 908, 268, 371 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 712, 908, 268, 371 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 712, 908, 268, 371 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 712, 908, 268, 371 is 1.
HCF(712, 908, 268, 371) = 1
HCF of 712, 908, 268, 371 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 712, 908, 268, 371 is 1.
Highest Common Factor of 712,908,268,371 is 1
Step 1: Since 908 > 712, we apply the division lemma to 908 and 712, to get
908 = 712 x 1 + 196
Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 196 and 712, to get
712 = 196 x 3 + 124
Step 3: We consider the new divisor 196 and the new remainder 124, and apply the division lemma to get
196 = 124 x 1 + 72
We consider the new divisor 124 and the new remainder 72,and apply the division lemma to get
124 = 72 x 1 + 52
We consider the new divisor 72 and the new remainder 52,and apply the division lemma to get
72 = 52 x 1 + 20
We consider the new divisor 52 and the new remainder 20,and apply the division lemma to get
52 = 20 x 2 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 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 712 and 908 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(52,20) = HCF(72,52) = HCF(124,72) = HCF(196,124) = HCF(712,196) = HCF(908,712) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 268 > 4, we apply the division lemma to 268 and 4, to get
268 = 4 x 67 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 268 is 4
Notice that 4 = HCF(268,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 371 > 4, we apply the division lemma to 371 and 4, to get
371 = 4 x 92 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 371 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(371,4) .
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Frequently Asked Questions on HCF of 712, 908, 268, 371 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 712, 908, 268, 371?
Answer: HCF of 712, 908, 268, 371 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 712, 908, 268, 371 using Euclid's Algorithm?
Answer: For arbitrary numbers 712, 908, 268, 371 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.