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 711, 451, 770 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 711, 451, 770 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 711, 451, 770 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 711, 451, 770 is 1.
HCF(711, 451, 770) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 711, 451, 770 is 1.
Step 1: Since 711 > 451, we apply the division lemma to 711 and 451, to get
711 = 451 x 1 + 260
Step 2: Since the reminder 451 ≠ 0, we apply division lemma to 260 and 451, to get
451 = 260 x 1 + 191
Step 3: We consider the new divisor 260 and the new remainder 191, and apply the division lemma to get
260 = 191 x 1 + 69
We consider the new divisor 191 and the new remainder 69,and apply the division lemma to get
191 = 69 x 2 + 53
We consider the new divisor 69 and the new remainder 53,and apply the division lemma to get
69 = 53 x 1 + 16
We consider the new divisor 53 and the new remainder 16,and apply the division lemma to get
53 = 16 x 3 + 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 711 and 451 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(53,16) = HCF(69,53) = HCF(191,69) = HCF(260,191) = HCF(451,260) = HCF(711,451) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 770 > 1, we apply the division lemma to 770 and 1, to get
770 = 1 x 770 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 770 is 1
Notice that 1 = HCF(770,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 711, 451, 770?
Answer: HCF of 711, 451, 770 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 711, 451, 770 using Euclid's Algorithm?
Answer: For arbitrary numbers 711, 451, 770 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.