Highest Common Factor of 672, 386, 714 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 672, 386, 714 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 672, 386, 714 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 672, 386, 714 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 672, 386, 714 is 2.
HCF(672, 386, 714) = 2
HCF of 672, 386, 714 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 672, 386, 714 is 2.
Highest Common Factor of 672,386,714 is 2
Step 1: Since 672 > 386, we apply the division lemma to 672 and 386, to get
672 = 386 x 1 + 286
Step 2: Since the reminder 386 ≠ 0, we apply division lemma to 286 and 386, to get
386 = 286 x 1 + 100
Step 3: We consider the new divisor 286 and the new remainder 100, and apply the division lemma to get
286 = 100 x 2 + 86
We consider the new divisor 100 and the new remainder 86,and apply the division lemma to get
100 = 86 x 1 + 14
We consider the new divisor 86 and the new remainder 14,and apply the division lemma to get
86 = 14 x 6 + 2
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 672 and 386 is 2
Notice that 2 = HCF(14,2) = HCF(86,14) = HCF(100,86) = HCF(286,100) = HCF(386,286) = HCF(672,386) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 714 > 2, we apply the division lemma to 714 and 2, to get
714 = 2 x 357 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 714 is 2
Notice that 2 = HCF(714,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 672, 386, 714 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 672, 386, 714?
Answer: HCF of 672, 386, 714 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 672, 386, 714 using Euclid's Algorithm?
Answer: For arbitrary numbers 672, 386, 714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.