Highest Common Factor of 1677, 3822, 74170 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 1677, 3822, 74170 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1677, 3822, 74170 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 1677, 3822, 74170 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 1677, 3822, 74170 is 1.
HCF(1677, 3822, 74170) = 1
HCF of 1677, 3822, 74170 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1677, 3822, 74170 is 1.
Highest Common Factor of 1677,3822,74170 is 1
Step 1: Since 3822 > 1677, we apply the division lemma to 3822 and 1677, to get
3822 = 1677 x 2 + 468
Step 2: Since the reminder 1677 ≠ 0, we apply division lemma to 468 and 1677, to get
1677 = 468 x 3 + 273
Step 3: We consider the new divisor 468 and the new remainder 273, and apply the division lemma to get
468 = 273 x 1 + 195
We consider the new divisor 273 and the new remainder 195,and apply the division lemma to get
273 = 195 x 1 + 78
We consider the new divisor 195 and the new remainder 78,and apply the division lemma to get
195 = 78 x 2 + 39
We consider the new divisor 78 and the new remainder 39,and apply the division lemma to get
78 = 39 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 39, the HCF of 1677 and 3822 is 39
Notice that 39 = HCF(78,39) = HCF(195,78) = HCF(273,195) = HCF(468,273) = HCF(1677,468) = HCF(3822,1677) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74170 > 39, we apply the division lemma to 74170 and 39, to get
74170 = 39 x 1901 + 31
Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 31 and 39, to get
39 = 31 x 1 + 8
Step 3: We consider the new divisor 31 and the new remainder 8, and apply the division lemma to get
31 = 8 x 3 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 39 and 74170 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(31,8) = HCF(39,31) = HCF(74170,39) .
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Frequently Asked Questions on HCF of 1677, 3822, 74170 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 1677, 3822, 74170?
Answer: HCF of 1677, 3822, 74170 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1677, 3822, 74170 using Euclid's Algorithm?
Answer: For arbitrary numbers 1677, 3822, 74170 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.