Highest Common Factor of 780, 274, 867 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 780, 274, 867 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 780, 274, 867 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 780, 274, 867 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 780, 274, 867 is 1.
HCF(780, 274, 867) = 1
HCF of 780, 274, 867 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 780, 274, 867 is 1.
Highest Common Factor of 780,274,867 is 1
Step 1: Since 780 > 274, we apply the division lemma to 780 and 274, to get
780 = 274 x 2 + 232
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 232 and 274, to get
274 = 232 x 1 + 42
Step 3: We consider the new divisor 232 and the new remainder 42, and apply the division lemma to get
232 = 42 x 5 + 22
We consider the new divisor 42 and the new remainder 22,and apply the division lemma to get
42 = 22 x 1 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 780 and 274 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(232,42) = HCF(274,232) = HCF(780,274) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 867 > 2, we apply the division lemma to 867 and 2, to get
867 = 2 x 433 + 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 867 is 1
Notice that 1 = HCF(2,1) = HCF(867,2) .
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Frequently Asked Questions on HCF of 780, 274, 867 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 780, 274, 867?
Answer: HCF of 780, 274, 867 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 780, 274, 867 using Euclid's Algorithm?
Answer: For arbitrary numbers 780, 274, 867 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
