Highest Common Factor of 1774, 6676, 74373 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 1774, 6676, 74373 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1774, 6676, 74373 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 1774, 6676, 74373 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 1774, 6676, 74373 is 1.
HCF(1774, 6676, 74373) = 1
HCF of 1774, 6676, 74373 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1774, 6676, 74373 is 1.
Highest Common Factor of 1774,6676,74373 is 1
Step 1: Since 6676 > 1774, we apply the division lemma to 6676 and 1774, to get
6676 = 1774 x 3 + 1354
Step 2: Since the reminder 1774 ≠ 0, we apply division lemma to 1354 and 1774, to get
1774 = 1354 x 1 + 420
Step 3: We consider the new divisor 1354 and the new remainder 420, and apply the division lemma to get
1354 = 420 x 3 + 94
We consider the new divisor 420 and the new remainder 94,and apply the division lemma to get
420 = 94 x 4 + 44
We consider the new divisor 94 and the new remainder 44,and apply the division lemma to get
94 = 44 x 2 + 6
We consider the new divisor 44 and the new remainder 6,and apply the division lemma to get
44 = 6 x 7 + 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 1774 and 6676 is 2
Notice that 2 = HCF(6,2) = HCF(44,6) = HCF(94,44) = HCF(420,94) = HCF(1354,420) = HCF(1774,1354) = HCF(6676,1774) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74373 > 2, we apply the division lemma to 74373 and 2, to get
74373 = 2 x 37186 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 74373 is 1
Notice that 1 = HCF(2,1) = HCF(74373,2) .
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Frequently Asked Questions on HCF of 1774, 6676, 74373 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 1774, 6676, 74373?
Answer: HCF of 1774, 6676, 74373 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1774, 6676, 74373 using Euclid's Algorithm?
Answer: For arbitrary numbers 1774, 6676, 74373 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.