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 771, 322, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 771, 322, 65 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 771, 322, 65 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 771, 322, 65 is 1.
HCF(771, 322, 65) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 771, 322, 65 is 1.
Step 1: Since 771 > 322, we apply the division lemma to 771 and 322, to get
771 = 322 x 2 + 127
Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 127 and 322, to get
322 = 127 x 2 + 68
Step 3: We consider the new divisor 127 and the new remainder 68, and apply the division lemma to get
127 = 68 x 1 + 59
We consider the new divisor 68 and the new remainder 59,and apply the division lemma to get
68 = 59 x 1 + 9
We consider the new divisor 59 and the new remainder 9,and apply the division lemma to get
59 = 9 x 6 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 771 and 322 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(59,9) = HCF(68,59) = HCF(127,68) = HCF(322,127) = HCF(771,322) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 1, we apply the division lemma to 65 and 1, to get
65 = 1 x 65 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 65 is 1
Notice that 1 = HCF(65,1) .
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 771, 322, 65?
Answer: HCF of 771, 322, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 771, 322, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 771, 322, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.