Highest Common Factor of 612, 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 612, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 612, 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 612, 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 612, 977 is 1.
HCF(612, 977) = 1
HCF of 612, 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 612, 977 is 1.
Highest Common Factor of 612,977 is 1
Step 1: Since 977 > 612, we apply the division lemma to 977 and 612, to get
977 = 612 x 1 + 365
Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 365 and 612, to get
612 = 365 x 1 + 247
Step 3: We consider the new divisor 365 and the new remainder 247, and apply the division lemma to get
365 = 247 x 1 + 118
We consider the new divisor 247 and the new remainder 118,and apply the division lemma to get
247 = 118 x 2 + 11
We consider the new divisor 118 and the new remainder 11,and apply the division lemma to get
118 = 11 x 10 + 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 612 and 977 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(118,11) = HCF(247,118) = HCF(365,247) = HCF(612,365) = HCF(977,612) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 612, 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 612, 977?
Answer: HCF of 612, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 612, 977 using Euclid's Algorithm?
Answer: For arbitrary numbers 612, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.