Highest Common Factor of 688, 3046, 4106 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 688, 3046, 4106 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 3046, 4106 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 688, 3046, 4106 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 688, 3046, 4106 is 2.
HCF(688, 3046, 4106) = 2
HCF of 688, 3046, 4106 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 688, 3046, 4106 is 2.
Highest Common Factor of 688,3046,4106 is 2
Step 1: Since 3046 > 688, we apply the division lemma to 3046 and 688, to get
3046 = 688 x 4 + 294
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 294 and 688, to get
688 = 294 x 2 + 100
Step 3: We consider the new divisor 294 and the new remainder 100, and apply the division lemma to get
294 = 100 x 2 + 94
We consider the new divisor 100 and the new remainder 94,and apply the division lemma to get
100 = 94 x 1 + 6
We consider the new divisor 94 and the new remainder 6,and apply the division lemma to get
94 = 6 x 15 + 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 688 and 3046 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(94,6) = HCF(100,94) = HCF(294,100) = HCF(688,294) = HCF(3046,688) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4106 > 2, we apply the division lemma to 4106 and 2, to get
4106 = 2 x 2053 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 4106 is 2
Notice that 2 = HCF(4106,2) .
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Frequently Asked Questions on HCF of 688, 3046, 4106 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 688, 3046, 4106?
Answer: HCF of 688, 3046, 4106 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 3046, 4106 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 3046, 4106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.