Highest Common Factor of 194, 637, 16 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 194, 637, 16 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 194, 637, 16 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 194, 637, 16 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 194, 637, 16 is 1.
HCF(194, 637, 16) = 1
HCF of 194, 637, 16 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 194, 637, 16 is 1.
Highest Common Factor of 194,637,16 is 1
Step 1: Since 637 > 194, we apply the division lemma to 637 and 194, to get
637 = 194 x 3 + 55
Step 2: Since the reminder 194 ≠ 0, we apply division lemma to 55 and 194, to get
194 = 55 x 3 + 29
Step 3: We consider the new divisor 55 and the new remainder 29, and apply the division lemma to get
55 = 29 x 1 + 26
We consider the new divisor 29 and the new remainder 26,and apply the division lemma to get
29 = 26 x 1 + 3
We consider the new divisor 26 and the new remainder 3,and apply the division lemma to get
26 = 3 x 8 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 194 and 637 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(26,3) = HCF(29,26) = HCF(55,29) = HCF(194,55) = HCF(637,194) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 1, we apply the division lemma to 16 and 1, to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 16 is 1
Notice that 1 = HCF(16,1) .
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Frequently Asked Questions on HCF of 194, 637, 16 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 194, 637, 16?
Answer: HCF of 194, 637, 16 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 194, 637, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 194, 637, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.