Highest Common Factor of 6076, 1078, 75746 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 6076, 1078, 75746 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6076, 1078, 75746 is 2 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 6076, 1078, 75746 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 6076, 1078, 75746 is 2.
HCF(6076, 1078, 75746) = 2
HCF of 6076, 1078, 75746 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6076, 1078, 75746 is 2.
Highest Common Factor of 6076,1078,75746 is 2
Step 1: Since 6076 > 1078, we apply the division lemma to 6076 and 1078, to get
6076 = 1078 x 5 + 686
Step 2: Since the reminder 1078 ≠ 0, we apply division lemma to 686 and 1078, to get
1078 = 686 x 1 + 392
Step 3: We consider the new divisor 686 and the new remainder 392, and apply the division lemma to get
686 = 392 x 1 + 294
We consider the new divisor 392 and the new remainder 294,and apply the division lemma to get
392 = 294 x 1 + 98
We consider the new divisor 294 and the new remainder 98,and apply the division lemma to get
294 = 98 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 98, the HCF of 6076 and 1078 is 98
Notice that 98 = HCF(294,98) = HCF(392,294) = HCF(686,392) = HCF(1078,686) = HCF(6076,1078) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 75746 > 98, we apply the division lemma to 75746 and 98, to get
75746 = 98 x 772 + 90
Step 2: Since the reminder 98 ≠ 0, we apply division lemma to 90 and 98, to get
98 = 90 x 1 + 8
Step 3: We consider the new divisor 90 and the new remainder 8, and apply the division lemma to get
90 = 8 x 11 + 2
We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 98 and 75746 is 2
Notice that 2 = HCF(8,2) = HCF(90,8) = HCF(98,90) = HCF(75746,98) .
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Frequently Asked Questions on HCF of 6076, 1078, 75746 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 6076, 1078, 75746?
Answer: HCF of 6076, 1078, 75746 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6076, 1078, 75746 using Euclid's Algorithm?
Answer: For arbitrary numbers 6076, 1078, 75746 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.