Highest Common Factor of 5991, 6778 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 5991, 6778 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 5991, 6778 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 5991, 6778 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 5991, 6778 is 1.
HCF(5991, 6778) = 1
HCF of 5991, 6778 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5991, 6778 is 1.
Highest Common Factor of 5991,6778 is 1
Step 1: Since 6778 > 5991, we apply the division lemma to 6778 and 5991, to get
6778 = 5991 x 1 + 787
Step 2: Since the reminder 5991 ≠ 0, we apply division lemma to 787 and 5991, to get
5991 = 787 x 7 + 482
Step 3: We consider the new divisor 787 and the new remainder 482, and apply the division lemma to get
787 = 482 x 1 + 305
We consider the new divisor 482 and the new remainder 305,and apply the division lemma to get
482 = 305 x 1 + 177
We consider the new divisor 305 and the new remainder 177,and apply the division lemma to get
305 = 177 x 1 + 128
We consider the new divisor 177 and the new remainder 128,and apply the division lemma to get
177 = 128 x 1 + 49
We consider the new divisor 128 and the new remainder 49,and apply the division lemma to get
128 = 49 x 2 + 30
We consider the new divisor 49 and the new remainder 30,and apply the division lemma to get
49 = 30 x 1 + 19
We consider the new divisor 30 and the new remainder 19,and apply the division lemma to get
30 = 19 x 1 + 11
We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get
19 = 11 x 1 + 8
We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get
11 = 8 x 1 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 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 5991 and 6778 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(30,19) = HCF(49,30) = HCF(128,49) = HCF(177,128) = HCF(305,177) = HCF(482,305) = HCF(787,482) = HCF(5991,787) = HCF(6778,5991) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 5991, 6778 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 5991, 6778?
Answer: HCF of 5991, 6778 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5991, 6778 using Euclid's Algorithm?
Answer: For arbitrary numbers 5991, 6778 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.