Highest Common Factor of 968, 214, 128 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 968, 214, 128 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 968, 214, 128 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 968, 214, 128 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 968, 214, 128 is 2.
HCF(968, 214, 128) = 2
HCF of 968, 214, 128 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 968, 214, 128 is 2.
Highest Common Factor of 968,214,128 is 2
Step 1: Since 968 > 214, we apply the division lemma to 968 and 214, to get
968 = 214 x 4 + 112
Step 2: Since the reminder 214 ≠ 0, we apply division lemma to 112 and 214, to get
214 = 112 x 1 + 102
Step 3: We consider the new divisor 112 and the new remainder 102, and apply the division lemma to get
112 = 102 x 1 + 10
We consider the new divisor 102 and the new remainder 10,and apply the division lemma to get
102 = 10 x 10 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 968 and 214 is 2
Notice that 2 = HCF(10,2) = HCF(102,10) = HCF(112,102) = HCF(214,112) = HCF(968,214) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 128 > 2, we apply the division lemma to 128 and 2, to get
128 = 2 x 64 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 128 is 2
Notice that 2 = HCF(128,2) .
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Frequently Asked Questions on HCF of 968, 214, 128 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 968, 214, 128?
Answer: HCF of 968, 214, 128 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 968, 214, 128 using Euclid's Algorithm?
Answer: For arbitrary numbers 968, 214, 128 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.