Highest Common Factor of 74, 54, 36, 209 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 74, 54, 36, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 74, 54, 36, 209 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 74, 54, 36, 209 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 74, 54, 36, 209 is 1.
HCF(74, 54, 36, 209) = 1
HCF of 74, 54, 36, 209 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 74, 54, 36, 209 is 1.
Highest Common Factor of 74,54,36,209 is 1
Step 1: Since 74 > 54, we apply the division lemma to 74 and 54, to get
74 = 54 x 1 + 20
Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 20 and 54, to get
54 = 20 x 2 + 14
Step 3: We consider the new divisor 20 and the new remainder 14, and apply the division lemma to get
20 = 14 x 1 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 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 74 and 54 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(54,20) = HCF(74,54) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 36 > 2, we apply the division lemma to 36 and 2, to get
36 = 2 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 36 is 2
Notice that 2 = HCF(36,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 209 > 2, we apply the division lemma to 209 and 2, to get
209 = 2 x 104 + 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 209 is 1
Notice that 1 = HCF(2,1) = HCF(209,2) .
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Frequently Asked Questions on HCF of 74, 54, 36, 209 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 74, 54, 36, 209?
Answer: HCF of 74, 54, 36, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 74, 54, 36, 209 using Euclid's Algorithm?
Answer: For arbitrary numbers 74, 54, 36, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.