Highest Common Factor of 808, 977 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 808, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 808, 977 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 808, 977 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 808, 977 is 1.
HCF(808, 977) = 1
HCF of 808, 977 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 808, 977 is 1.
Highest Common Factor of 808,977 is 1
Step 1: Since 977 > 808, we apply the division lemma to 977 and 808, to get
977 = 808 x 1 + 169
Step 2: Since the reminder 808 ≠ 0, we apply division lemma to 169 and 808, to get
808 = 169 x 4 + 132
Step 3: We consider the new divisor 169 and the new remainder 132, and apply the division lemma to get
169 = 132 x 1 + 37
We consider the new divisor 132 and the new remainder 37,and apply the division lemma to get
132 = 37 x 3 + 21
We consider the new divisor 37 and the new remainder 21,and apply the division lemma to get
37 = 21 x 1 + 16
We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get
21 = 16 x 1 + 5
We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get
16 = 5 x 3 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 808 and 977 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(37,21) = HCF(132,37) = HCF(169,132) = HCF(808,169) = HCF(977,808) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 808, 977 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 808, 977?
Answer: HCF of 808, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 808, 977 using Euclid's Algorithm?
Answer: For arbitrary numbers 808, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.