Highest Common Factor of 777, 267, 723 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 777, 267, 723 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 777, 267, 723 is 3 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 777, 267, 723 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 777, 267, 723 is 3.
HCF(777, 267, 723) = 3
HCF of 777, 267, 723 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 777, 267, 723 is 3.
Highest Common Factor of 777,267,723 is 3
Step 1: Since 777 > 267, we apply the division lemma to 777 and 267, to get
777 = 267 x 2 + 243
Step 2: Since the reminder 267 ≠ 0, we apply division lemma to 243 and 267, to get
267 = 243 x 1 + 24
Step 3: We consider the new divisor 243 and the new remainder 24, and apply the division lemma to get
243 = 24 x 10 + 3
We consider the new divisor 24 and the new remainder 3, and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 777 and 267 is 3
Notice that 3 = HCF(24,3) = HCF(243,24) = HCF(267,243) = HCF(777,267) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 723 > 3, we apply the division lemma to 723 and 3, to get
723 = 3 x 241 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 723 is 3
Notice that 3 = HCF(723,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 777, 267, 723 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 777, 267, 723?
Answer: HCF of 777, 267, 723 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 777, 267, 723 using Euclid's Algorithm?
Answer: For arbitrary numbers 777, 267, 723 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.