Highest Common Factor of 746, 678, 114 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 746, 678, 114 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 746, 678, 114 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 746, 678, 114 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 746, 678, 114 is 2.
HCF(746, 678, 114) = 2
HCF of 746, 678, 114 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 746, 678, 114 is 2.
Highest Common Factor of 746,678,114 is 2
Step 1: Since 746 > 678, we apply the division lemma to 746 and 678, to get
746 = 678 x 1 + 68
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 68 and 678, to get
678 = 68 x 9 + 66
Step 3: We consider the new divisor 68 and the new remainder 66, and apply the division lemma to get
68 = 66 x 1 + 2
We consider the new divisor 66 and the new remainder 2, and apply the division lemma to get
66 = 2 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 746 and 678 is 2
Notice that 2 = HCF(66,2) = HCF(68,66) = HCF(678,68) = HCF(746,678) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 114 > 2, we apply the division lemma to 114 and 2, to get
114 = 2 x 57 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 114 is 2
Notice that 2 = HCF(114,2) .
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Frequently Asked Questions on HCF of 746, 678, 114 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 746, 678, 114?
Answer: HCF of 746, 678, 114 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 746, 678, 114 using Euclid's Algorithm?
Answer: For arbitrary numbers 746, 678, 114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.