Highest Common Factor of 1406, 2056 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 1406, 2056 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1406, 2056 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 1406, 2056 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 1406, 2056 is 2.
HCF(1406, 2056) = 2
HCF of 1406, 2056 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1406, 2056 is 2.
Highest Common Factor of 1406,2056 is 2
Step 1: Since 2056 > 1406, we apply the division lemma to 2056 and 1406, to get
2056 = 1406 x 1 + 650
Step 2: Since the reminder 1406 ≠ 0, we apply division lemma to 650 and 1406, to get
1406 = 650 x 2 + 106
Step 3: We consider the new divisor 650 and the new remainder 106, and apply the division lemma to get
650 = 106 x 6 + 14
We consider the new divisor 106 and the new remainder 14,and apply the division lemma to get
106 = 14 x 7 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1406 and 2056 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(106,14) = HCF(650,106) = HCF(1406,650) = HCF(2056,1406) .
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Frequently Asked Questions on HCF of 1406, 2056 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 1406, 2056?
Answer: HCF of 1406, 2056 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1406, 2056 using Euclid's Algorithm?
Answer: For arbitrary numbers 1406, 2056 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.