Highest Common Factor of 864, 720, 894 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, 720, 894 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 864, 720, 894 is 6 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, 720, 894 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, 720, 894 is 6.
HCF(864, 720, 894) = 6
HCF of 864, 720, 894 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, 720, 894 is 6.
Highest Common Factor of 864,720,894 is 6
Step 1: Since 864 > 720, we apply the division lemma to 864 and 720, to get
864 = 720 x 1 + 144
Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 144 and 720, to get
720 = 144 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 144, the HCF of 864 and 720 is 144
Notice that 144 = HCF(720,144) = HCF(864,720) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 894 > 144, we apply the division lemma to 894 and 144, to get
894 = 144 x 6 + 30
Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 30 and 144, to get
144 = 30 x 4 + 24
Step 3: We consider the new divisor 30 and the new remainder 24, and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6, and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 144 and 894 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(144,30) = HCF(894,144) .
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Frequently Asked Questions on HCF of 864, 720, 894 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, 720, 894?
Answer: HCF of 864, 720, 894 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 864, 720, 894 using Euclid's Algorithm?
Answer: For arbitrary numbers 864, 720, 894 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.