Highest Common Factor of 864, 336, 677 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, 336, 677 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 864, 336, 677 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, 336, 677 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, 336, 677 is 1.
HCF(864, 336, 677) = 1
HCF of 864, 336, 677 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, 336, 677 is 1.
Highest Common Factor of 864,336,677 is 1
Step 1: Since 864 > 336, we apply the division lemma to 864 and 336, to get
864 = 336 x 2 + 192
Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 192 and 336, to get
336 = 192 x 1 + 144
Step 3: We consider the new divisor 192 and the new remainder 144, and apply the division lemma to get
192 = 144 x 1 + 48
We consider the new divisor 144 and the new remainder 48, and apply the division lemma to get
144 = 48 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 48, the HCF of 864 and 336 is 48
Notice that 48 = HCF(144,48) = HCF(192,144) = HCF(336,192) = HCF(864,336) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 677 > 48, we apply the division lemma to 677 and 48, to get
677 = 48 x 14 + 5
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 5 and 48, to get
48 = 5 x 9 + 3
Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 48 and 677 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(48,5) = HCF(677,48) .
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Frequently Asked Questions on HCF of 864, 336, 677 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, 336, 677?
Answer: HCF of 864, 336, 677 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 864, 336, 677 using Euclid's Algorithm?
Answer: For arbitrary numbers 864, 336, 677 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.