Highest Common Factor of 864, 960, 156 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, 960, 156 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 864, 960, 156 is 12 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, 960, 156 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, 960, 156 is 12.
HCF(864, 960, 156) = 12
HCF of 864, 960, 156 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, 960, 156 is 12.
Highest Common Factor of 864,960,156 is 12
Step 1: Since 960 > 864, we apply the division lemma to 960 and 864, to get
960 = 864 x 1 + 96
Step 2: Since the reminder 864 ≠ 0, we apply division lemma to 96 and 864, to get
864 = 96 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 96, the HCF of 864 and 960 is 96
Notice that 96 = HCF(864,96) = HCF(960,864) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 156 > 96, we apply the division lemma to 156 and 96, to get
156 = 96 x 1 + 60
Step 2: Since the reminder 96 ≠ 0, we apply division lemma to 60 and 96, to get
96 = 60 x 1 + 36
Step 3: We consider the new divisor 60 and the new remainder 36, and apply the division lemma to get
60 = 36 x 1 + 24
We consider the new divisor 36 and the new remainder 24,and apply the division lemma to get
36 = 24 x 1 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 96 and 156 is 12
Notice that 12 = HCF(24,12) = HCF(36,24) = HCF(60,36) = HCF(96,60) = HCF(156,96) .
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Frequently Asked Questions on HCF of 864, 960, 156 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, 960, 156?
Answer: HCF of 864, 960, 156 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 864, 960, 156 using Euclid's Algorithm?
Answer: For arbitrary numbers 864, 960, 156 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
