Highest Common Factor of 1416, 2606 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 1416, 2606 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1416, 2606 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 1416, 2606 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 1416, 2606 is 2.
HCF(1416, 2606) = 2
HCF of 1416, 2606 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1416, 2606 is 2.
Highest Common Factor of 1416,2606 is 2
Step 1: Since 2606 > 1416, we apply the division lemma to 2606 and 1416, to get
2606 = 1416 x 1 + 1190
Step 2: Since the reminder 1416 ≠ 0, we apply division lemma to 1190 and 1416, to get
1416 = 1190 x 1 + 226
Step 3: We consider the new divisor 1190 and the new remainder 226, and apply the division lemma to get
1190 = 226 x 5 + 60
We consider the new divisor 226 and the new remainder 60,and apply the division lemma to get
226 = 60 x 3 + 46
We consider the new divisor 60 and the new remainder 46,and apply the division lemma to get
60 = 46 x 1 + 14
We consider the new divisor 46 and the new remainder 14,and apply the division lemma to get
46 = 14 x 3 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 1416 and 2606 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(46,14) = HCF(60,46) = HCF(226,60) = HCF(1190,226) = HCF(1416,1190) = HCF(2606,1416) .
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Frequently Asked Questions on HCF of 1416, 2606 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 1416, 2606?
Answer: HCF of 1416, 2606 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1416, 2606 using Euclid's Algorithm?
Answer: For arbitrary numbers 1416, 2606 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.