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, 386, 678 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 968, 386, 678 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, 386, 678 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, 386, 678 is 2.
HCF(968, 386, 678) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 968, 386, 678 is 2.
Step 1: Since 968 > 386, we apply the division lemma to 968 and 386, to get
968 = 386 x 2 + 196
Step 2: Since the reminder 386 ≠ 0, we apply division lemma to 196 and 386, to get
386 = 196 x 1 + 190
Step 3: We consider the new divisor 196 and the new remainder 190, and apply the division lemma to get
196 = 190 x 1 + 6
We consider the new divisor 190 and the new remainder 6,and apply the division lemma to get
190 = 6 x 31 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 968 and 386 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(190,6) = HCF(196,190) = HCF(386,196) = HCF(968,386) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 678 > 2, we apply the division lemma to 678 and 2, to get
678 = 2 x 339 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 678 is 2
Notice that 2 = HCF(678,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 386, 678?
Answer: HCF of 968, 386, 678 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 968, 386, 678 using Euclid's Algorithm?
Answer: For arbitrary numbers 968, 386, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.