Highest Common Factor of 69, 87, 302, 204 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 69, 87, 302, 204 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 69, 87, 302, 204 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 69, 87, 302, 204 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 69, 87, 302, 204 is 1.
HCF(69, 87, 302, 204) = 1
HCF of 69, 87, 302, 204 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 69, 87, 302, 204 is 1.
Highest Common Factor of 69,87,302,204 is 1
Step 1: Since 87 > 69, we apply the division lemma to 87 and 69, to get
87 = 69 x 1 + 18
Step 2: Since the reminder 69 ≠ 0, we apply division lemma to 18 and 69, to get
69 = 18 x 3 + 15
Step 3: We consider the new divisor 18 and the new remainder 15, and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3, and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 69 and 87 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(69,18) = HCF(87,69) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 302 > 3, we apply the division lemma to 302 and 3, to get
302 = 3 x 100 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 302 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(302,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 204 > 1, we apply the division lemma to 204 and 1, to get
204 = 1 x 204 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 204 is 1
Notice that 1 = HCF(204,1) .
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Frequently Asked Questions on HCF of 69, 87, 302, 204 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 69, 87, 302, 204?
Answer: HCF of 69, 87, 302, 204 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 69, 87, 302, 204 using Euclid's Algorithm?
Answer: For arbitrary numbers 69, 87, 302, 204 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.