Highest Common Factor of 774, 55138 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 774, 55138 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 774, 55138 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 774, 55138 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 774, 55138 is 2.
HCF(774, 55138) = 2
HCF of 774, 55138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 774, 55138 is 2.
Highest Common Factor of 774,55138 is 2
Step 1: Since 55138 > 774, we apply the division lemma to 55138 and 774, to get
55138 = 774 x 71 + 184
Step 2: Since the reminder 774 ≠ 0, we apply division lemma to 184 and 774, to get
774 = 184 x 4 + 38
Step 3: We consider the new divisor 184 and the new remainder 38, and apply the division lemma to get
184 = 38 x 4 + 32
We consider the new divisor 38 and the new remainder 32,and apply the division lemma to get
38 = 32 x 1 + 6
We consider the new divisor 32 and the new remainder 6,and apply the division lemma to get
32 = 6 x 5 + 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 774 and 55138 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(38,32) = HCF(184,38) = HCF(774,184) = HCF(55138,774) .
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Frequently Asked Questions on HCF of 774, 55138 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 774, 55138?
Answer: HCF of 774, 55138 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 774, 55138 using Euclid's Algorithm?
Answer: For arbitrary numbers 774, 55138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.