Highest Common Factor of 1606, 6768 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 1606, 6768 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1606, 6768 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 1606, 6768 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 1606, 6768 is 2.
HCF(1606, 6768) = 2
HCF of 1606, 6768 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1606, 6768 is 2.
Highest Common Factor of 1606,6768 is 2
Step 1: Since 6768 > 1606, we apply the division lemma to 6768 and 1606, to get
6768 = 1606 x 4 + 344
Step 2: Since the reminder 1606 ≠ 0, we apply division lemma to 344 and 1606, to get
1606 = 344 x 4 + 230
Step 3: We consider the new divisor 344 and the new remainder 230, and apply the division lemma to get
344 = 230 x 1 + 114
We consider the new divisor 230 and the new remainder 114,and apply the division lemma to get
230 = 114 x 2 + 2
We consider the new divisor 114 and the new remainder 2,and apply the division lemma to get
114 = 2 x 57 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1606 and 6768 is 2
Notice that 2 = HCF(114,2) = HCF(230,114) = HCF(344,230) = HCF(1606,344) = HCF(6768,1606) .
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Frequently Asked Questions on HCF of 1606, 6768 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 1606, 6768?
Answer: HCF of 1606, 6768 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1606, 6768 using Euclid's Algorithm?
Answer: For arbitrary numbers 1606, 6768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.