Highest Common Factor of 112, 960, 814 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 112, 960, 814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 112, 960, 814 is 2 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 112, 960, 814 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 112, 960, 814 is 2.
HCF(112, 960, 814) = 2
HCF of 112, 960, 814 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 112, 960, 814 is 2.
Highest Common Factor of 112,960,814 is 2
Step 1: Since 960 > 112, we apply the division lemma to 960 and 112, to get
960 = 112 x 8 + 64
Step 2: Since the reminder 112 ≠ 0, we apply division lemma to 64 and 112, to get
112 = 64 x 1 + 48
Step 3: We consider the new divisor 64 and the new remainder 48, and apply the division lemma to get
64 = 48 x 1 + 16
We consider the new divisor 48 and the new remainder 16, and apply the division lemma to get
48 = 16 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 112 and 960 is 16
Notice that 16 = HCF(48,16) = HCF(64,48) = HCF(112,64) = HCF(960,112) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 814 > 16, we apply the division lemma to 814 and 16, to get
814 = 16 x 50 + 14
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 14 and 16, to get
16 = 14 x 1 + 2
Step 3: We consider the new divisor 14 and the new remainder 2, and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 814 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(814,16) .
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Frequently Asked Questions on HCF of 112, 960, 814 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 112, 960, 814?
Answer: HCF of 112, 960, 814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 112, 960, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 112, 960, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
