Highest Common Factor of 771, 3678 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 771, 3678 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 771, 3678 is 3 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 771, 3678 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 771, 3678 is 3.
HCF(771, 3678) = 3
HCF of 771, 3678 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 771, 3678 is 3.
Highest Common Factor of 771,3678 is 3
Step 1: Since 3678 > 771, we apply the division lemma to 3678 and 771, to get
3678 = 771 x 4 + 594
Step 2: Since the reminder 771 ≠ 0, we apply division lemma to 594 and 771, to get
771 = 594 x 1 + 177
Step 3: We consider the new divisor 594 and the new remainder 177, and apply the division lemma to get
594 = 177 x 3 + 63
We consider the new divisor 177 and the new remainder 63,and apply the division lemma to get
177 = 63 x 2 + 51
We consider the new divisor 63 and the new remainder 51,and apply the division lemma to get
63 = 51 x 1 + 12
We consider the new divisor 51 and the new remainder 12,and apply the division lemma to get
51 = 12 x 4 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 771 and 3678 is 3
Notice that 3 = HCF(12,3) = HCF(51,12) = HCF(63,51) = HCF(177,63) = HCF(594,177) = HCF(771,594) = HCF(3678,771) .
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Frequently Asked Questions on HCF of 771, 3678 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 771, 3678?
Answer: HCF of 771, 3678 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 771, 3678 using Euclid's Algorithm?
Answer: For arbitrary numbers 771, 3678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
