Highest Common Factor of 667, 1776 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 667, 1776 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 667, 1776 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 667, 1776 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 667, 1776 is 1.
HCF(667, 1776) = 1
HCF of 667, 1776 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 667, 1776 is 1.
Highest Common Factor of 667,1776 is 1
Step 1: Since 1776 > 667, we apply the division lemma to 1776 and 667, to get
1776 = 667 x 2 + 442
Step 2: Since the reminder 667 ≠ 0, we apply division lemma to 442 and 667, to get
667 = 442 x 1 + 225
Step 3: We consider the new divisor 442 and the new remainder 225, and apply the division lemma to get
442 = 225 x 1 + 217
We consider the new divisor 225 and the new remainder 217,and apply the division lemma to get
225 = 217 x 1 + 8
We consider the new divisor 217 and the new remainder 8,and apply the division lemma to get
217 = 8 x 27 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 667 and 1776 is 1
Notice that 1 = HCF(8,1) = HCF(217,8) = HCF(225,217) = HCF(442,225) = HCF(667,442) = HCF(1776,667) .
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Frequently Asked Questions on HCF of 667, 1776 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 667, 1776?
Answer: HCF of 667, 1776 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 667, 1776 using Euclid's Algorithm?
Answer: For arbitrary numbers 667, 1776 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.