Highest Common Factor of 78, 50, 14, 827 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 78, 50, 14, 827 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 78, 50, 14, 827 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 78, 50, 14, 827 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 78, 50, 14, 827 is 1.
HCF(78, 50, 14, 827) = 1
HCF of 78, 50, 14, 827 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 78, 50, 14, 827 is 1.
Highest Common Factor of 78,50,14,827 is 1
Step 1: Since 78 > 50, we apply the division lemma to 78 and 50, to get
78 = 50 x 1 + 28
Step 2: Since the reminder 50 ≠ 0, we apply division lemma to 28 and 50, to get
50 = 28 x 1 + 22
Step 3: We consider the new divisor 28 and the new remainder 22, and apply the division lemma to get
28 = 22 x 1 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 78 and 50 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(50,28) = HCF(78,50) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14 > 2, we apply the division lemma to 14 and 2, to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 14 is 2
Notice that 2 = HCF(14,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 827 > 2, we apply the division lemma to 827 and 2, to get
827 = 2 x 413 + 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 827 is 1
Notice that 1 = HCF(2,1) = HCF(827,2) .
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Frequently Asked Questions on HCF of 78, 50, 14, 827 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 78, 50, 14, 827?
Answer: HCF of 78, 50, 14, 827 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 78, 50, 14, 827 using Euclid's Algorithm?
Answer: For arbitrary numbers 78, 50, 14, 827 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.