Highest Common Factor of 686, 333, 108, 42 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, 333, 108, 42 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 686, 333, 108, 42 is 1 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, 333, 108, 42 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, 333, 108, 42 is 1.
HCF(686, 333, 108, 42) = 1
HCF of 686, 333, 108, 42 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, 333, 108, 42 is 1.
Highest Common Factor of 686,333,108,42 is 1
Step 1: Since 686 > 333, we apply the division lemma to 686 and 333, to get
686 = 333 x 2 + 20
Step 2: Since the reminder 333 ≠ 0, we apply division lemma to 20 and 333, to get
333 = 20 x 16 + 13
Step 3: We consider the new divisor 20 and the new remainder 13, and apply the division lemma to get
20 = 13 x 1 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 686 and 333 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(333,20) = HCF(686,333) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 108 > 1, we apply the division lemma to 108 and 1, to get
108 = 1 x 108 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 108 is 1
Notice that 1 = HCF(108,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 1, we apply the division lemma to 42 and 1, to get
42 = 1 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42 is 1
Notice that 1 = HCF(42,1) .
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Frequently Asked Questions on HCF of 686, 333, 108, 42 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, 333, 108, 42?
Answer: HCF of 686, 333, 108, 42 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 686, 333, 108, 42 using Euclid's Algorithm?
Answer: For arbitrary numbers 686, 333, 108, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
