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 864, 68, 696, 737 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 864, 68, 696, 737 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 864, 68, 696, 737 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 864, 68, 696, 737 is 1.
HCF(864, 68, 696, 737) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 864, 68, 696, 737 is 1.
Step 1: Since 864 > 68, we apply the division lemma to 864 and 68, to get
864 = 68 x 12 + 48
Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 48 and 68, to get
68 = 48 x 1 + 20
Step 3: We consider the new divisor 48 and the new remainder 20, and apply the division lemma to get
48 = 20 x 2 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 864 and 68 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(48,20) = HCF(68,48) = HCF(864,68) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 696 > 4, we apply the division lemma to 696 and 4, to get
696 = 4 x 174 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 696 is 4
Notice that 4 = HCF(696,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 737 > 4, we apply the division lemma to 737 and 4, to get
737 = 4 x 184 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 737 is 1
Notice that 1 = HCF(4,1) = HCF(737,4) .
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 864, 68, 696, 737?
Answer: HCF of 864, 68, 696, 737 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 864, 68, 696, 737 using Euclid's Algorithm?
Answer: For arbitrary numbers 864, 68, 696, 737 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.