Highest Common Factor of 168, 8208, 2657 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 168, 8208, 2657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 168, 8208, 2657 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 168, 8208, 2657 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 168, 8208, 2657 is 1.
HCF(168, 8208, 2657) = 1
HCF of 168, 8208, 2657 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 168, 8208, 2657 is 1.
Highest Common Factor of 168,8208,2657 is 1
Step 1: Since 8208 > 168, we apply the division lemma to 8208 and 168, to get
8208 = 168 x 48 + 144
Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 144 and 168, to get
168 = 144 x 1 + 24
Step 3: We consider the new divisor 144 and the new remainder 24, and apply the division lemma to get
144 = 24 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 168 and 8208 is 24
Notice that 24 = HCF(144,24) = HCF(168,144) = HCF(8208,168) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2657 > 24, we apply the division lemma to 2657 and 24, to get
2657 = 24 x 110 + 17
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 17 and 24, to get
24 = 17 x 1 + 7
Step 3: We consider the new divisor 17 and the new remainder 7, and apply the division lemma to get
17 = 7 x 2 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 24 and 2657 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(24,17) = HCF(2657,24) .
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Frequently Asked Questions on HCF of 168, 8208, 2657 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 168, 8208, 2657?
Answer: HCF of 168, 8208, 2657 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 168, 8208, 2657 using Euclid's Algorithm?
Answer: For arbitrary numbers 168, 8208, 2657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
