Highest Common Factor of 778, 307 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 778, 307 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 778, 307 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 778, 307 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 778, 307 is 1.
HCF(778, 307) = 1
HCF of 778, 307 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 778, 307 is 1.
Highest Common Factor of 778,307 is 1
Step 1: Since 778 > 307, we apply the division lemma to 778 and 307, to get
778 = 307 x 2 + 164
Step 2: Since the reminder 307 ≠ 0, we apply division lemma to 164 and 307, to get
307 = 164 x 1 + 143
Step 3: We consider the new divisor 164 and the new remainder 143, and apply the division lemma to get
164 = 143 x 1 + 21
We consider the new divisor 143 and the new remainder 21,and apply the division lemma to get
143 = 21 x 6 + 17
We consider the new divisor 21 and the new remainder 17,and apply the division lemma to get
21 = 17 x 1 + 4
We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get
17 = 4 x 4 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 778 and 307 is 1
Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(21,17) = HCF(143,21) = HCF(164,143) = HCF(307,164) = HCF(778,307) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 778, 307 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 778, 307?
Answer: HCF of 778, 307 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 778, 307 using Euclid's Algorithm?
Answer: For arbitrary numbers 778, 307 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.