Highest Common Factor of 674, 34135 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 674, 34135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 674, 34135 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 674, 34135 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 674, 34135 is 1.
HCF(674, 34135) = 1
HCF of 674, 34135 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 674, 34135 is 1.
Highest Common Factor of 674,34135 is 1
Step 1: Since 34135 > 674, we apply the division lemma to 34135 and 674, to get
34135 = 674 x 50 + 435
Step 2: Since the reminder 674 ≠ 0, we apply division lemma to 435 and 674, to get
674 = 435 x 1 + 239
Step 3: We consider the new divisor 435 and the new remainder 239, and apply the division lemma to get
435 = 239 x 1 + 196
We consider the new divisor 239 and the new remainder 196,and apply the division lemma to get
239 = 196 x 1 + 43
We consider the new divisor 196 and the new remainder 43,and apply the division lemma to get
196 = 43 x 4 + 24
We consider the new divisor 43 and the new remainder 24,and apply the division lemma to get
43 = 24 x 1 + 19
We consider the new divisor 24 and the new remainder 19,and apply the division lemma to get
24 = 19 x 1 + 5
We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get
19 = 5 x 3 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 674 and 34135 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(24,19) = HCF(43,24) = HCF(196,43) = HCF(239,196) = HCF(435,239) = HCF(674,435) = HCF(34135,674) .
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Frequently Asked Questions on HCF of 674, 34135 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 674, 34135?
Answer: HCF of 674, 34135 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 674, 34135 using Euclid's Algorithm?
Answer: For arbitrary numbers 674, 34135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
