Highest Common Factor of 8945, 3414 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 8945, 3414 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8945, 3414 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 8945, 3414 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 8945, 3414 is 1.
HCF(8945, 3414) = 1
HCF of 8945, 3414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8945, 3414 is 1.
Highest Common Factor of 8945,3414 is 1
Step 1: Since 8945 > 3414, we apply the division lemma to 8945 and 3414, to get
8945 = 3414 x 2 + 2117
Step 2: Since the reminder 3414 ≠ 0, we apply division lemma to 2117 and 3414, to get
3414 = 2117 x 1 + 1297
Step 3: We consider the new divisor 2117 and the new remainder 1297, and apply the division lemma to get
2117 = 1297 x 1 + 820
We consider the new divisor 1297 and the new remainder 820,and apply the division lemma to get
1297 = 820 x 1 + 477
We consider the new divisor 820 and the new remainder 477,and apply the division lemma to get
820 = 477 x 1 + 343
We consider the new divisor 477 and the new remainder 343,and apply the division lemma to get
477 = 343 x 1 + 134
We consider the new divisor 343 and the new remainder 134,and apply the division lemma to get
343 = 134 x 2 + 75
We consider the new divisor 134 and the new remainder 75,and apply the division lemma to get
134 = 75 x 1 + 59
We consider the new divisor 75 and the new remainder 59,and apply the division lemma to get
75 = 59 x 1 + 16
We consider the new divisor 59 and the new remainder 16,and apply the division lemma to get
59 = 16 x 3 + 11
We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get
16 = 11 x 1 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8945 and 3414 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(59,16) = HCF(75,59) = HCF(134,75) = HCF(343,134) = HCF(477,343) = HCF(820,477) = HCF(1297,820) = HCF(2117,1297) = HCF(3414,2117) = HCF(8945,3414) .
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Frequently Asked Questions on HCF of 8945, 3414 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 8945, 3414?
Answer: HCF of 8945, 3414 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8945, 3414 using Euclid's Algorithm?
Answer: For arbitrary numbers 8945, 3414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
