Highest Common Factor of 774, 42371 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, 42371 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 774, 42371 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 774, 42371 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, 42371 is 1.
HCF(774, 42371) = 1
HCF of 774, 42371 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, 42371 is 1.
Highest Common Factor of 774,42371 is 1
Step 1: Since 42371 > 774, we apply the division lemma to 42371 and 774, to get
42371 = 774 x 54 + 575
Step 2: Since the reminder 774 ≠ 0, we apply division lemma to 575 and 774, to get
774 = 575 x 1 + 199
Step 3: We consider the new divisor 575 and the new remainder 199, and apply the division lemma to get
575 = 199 x 2 + 177
We consider the new divisor 199 and the new remainder 177,and apply the division lemma to get
199 = 177 x 1 + 22
We consider the new divisor 177 and the new remainder 22,and apply the division lemma to get
177 = 22 x 8 + 1
We consider the new divisor 22 and the new remainder 1,and apply the division lemma to get
22 = 1 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 774 and 42371 is 1
Notice that 1 = HCF(22,1) = HCF(177,22) = HCF(199,177) = HCF(575,199) = HCF(774,575) = HCF(42371,774) .
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Frequently Asked Questions on HCF of 774, 42371 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, 42371?
Answer: HCF of 774, 42371 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 774, 42371 using Euclid's Algorithm?
Answer: For arbitrary numbers 774, 42371 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.