Highest Common Factor of 686, 448, 882 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 686, 448, 882 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 686, 448, 882 is 14 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 686, 448, 882 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 686, 448, 882 is 14.
HCF(686, 448, 882) = 14
HCF of 686, 448, 882 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 686, 448, 882 is 14.
Highest Common Factor of 686,448,882 is 14
Step 1: Since 686 > 448, we apply the division lemma to 686 and 448, to get
686 = 448 x 1 + 238
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 238 and 448, to get
448 = 238 x 1 + 210
Step 3: We consider the new divisor 238 and the new remainder 210, and apply the division lemma to get
238 = 210 x 1 + 28
We consider the new divisor 210 and the new remainder 28,and apply the division lemma to get
210 = 28 x 7 + 14
We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 686 and 448 is 14
Notice that 14 = HCF(28,14) = HCF(210,28) = HCF(238,210) = HCF(448,238) = HCF(686,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 882 > 14, we apply the division lemma to 882 and 14, to get
882 = 14 x 63 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 14 and 882 is 14
Notice that 14 = HCF(882,14) .
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Frequently Asked Questions on HCF of 686, 448, 882 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 686, 448, 882?
Answer: HCF of 686, 448, 882 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 686, 448, 882 using Euclid's Algorithm?
Answer: For arbitrary numbers 686, 448, 882 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
