Highest Common Factor of 864, 320, 103, 869 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 864, 320, 103, 869 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 864, 320, 103, 869 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, 320, 103, 869 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, 320, 103, 869 is 1.
HCF(864, 320, 103, 869) = 1
HCF of 864, 320, 103, 869 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 864, 320, 103, 869 is 1.
Highest Common Factor of 864,320,103,869 is 1
Step 1: Since 864 > 320, we apply the division lemma to 864 and 320, to get
864 = 320 x 2 + 224
Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 224 and 320, to get
320 = 224 x 1 + 96
Step 3: We consider the new divisor 224 and the new remainder 96, and apply the division lemma to get
224 = 96 x 2 + 32
We consider the new divisor 96 and the new remainder 32, and apply the division lemma to get
96 = 32 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 864 and 320 is 32
Notice that 32 = HCF(96,32) = HCF(224,96) = HCF(320,224) = HCF(864,320) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 103 > 32, we apply the division lemma to 103 and 32, to get
103 = 32 x 3 + 7
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 7 and 32, to get
32 = 7 x 4 + 4
Step 3: We consider the new divisor 7 and the new remainder 4, and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 32 and 103 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(32,7) = HCF(103,32) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 869 > 1, we apply the division lemma to 869 and 1, to get
869 = 1 x 869 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 869 is 1
Notice that 1 = HCF(869,1) .
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Frequently Asked Questions on HCF of 864, 320, 103, 869 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 864, 320, 103, 869?
Answer: HCF of 864, 320, 103, 869 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 864, 320, 103, 869 using Euclid's Algorithm?
Answer: For arbitrary numbers 864, 320, 103, 869 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.