Highest Common Factor of 506, 7769 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 506, 7769 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 506, 7769 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 506, 7769 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 506, 7769 is 1.
HCF(506, 7769) = 1
HCF of 506, 7769 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 506, 7769 is 1.
Highest Common Factor of 506,7769 is 1
Step 1: Since 7769 > 506, we apply the division lemma to 7769 and 506, to get
7769 = 506 x 15 + 179
Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 179 and 506, to get
506 = 179 x 2 + 148
Step 3: We consider the new divisor 179 and the new remainder 148, and apply the division lemma to get
179 = 148 x 1 + 31
We consider the new divisor 148 and the new remainder 31,and apply the division lemma to get
148 = 31 x 4 + 24
We consider the new divisor 31 and the new remainder 24,and apply the division lemma to get
31 = 24 x 1 + 7
We consider the new divisor 24 and the new remainder 7,and apply the division lemma to get
24 = 7 x 3 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 506 and 7769 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(24,7) = HCF(31,24) = HCF(148,31) = HCF(179,148) = HCF(506,179) = HCF(7769,506) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 506, 7769 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 506, 7769?
Answer: HCF of 506, 7769 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 506, 7769 using Euclid's Algorithm?
Answer: For arbitrary numbers 506, 7769 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
