Highest Common Factor of 780, 676, 860 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, 676, 860 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 780, 676, 860 is 4 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, 676, 860 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, 676, 860 is 4.
HCF(780, 676, 860) = 4
HCF of 780, 676, 860 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, 676, 860 is 4.
Highest Common Factor of 780,676,860 is 4
Step 1: Since 780 > 676, we apply the division lemma to 780 and 676, to get
780 = 676 x 1 + 104
Step 2: Since the reminder 676 ≠ 0, we apply division lemma to 104 and 676, to get
676 = 104 x 6 + 52
Step 3: We consider the new divisor 104 and the new remainder 52, and apply the division lemma to get
104 = 52 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 52, the HCF of 780 and 676 is 52
Notice that 52 = HCF(104,52) = HCF(676,104) = HCF(780,676) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 860 > 52, we apply the division lemma to 860 and 52, to get
860 = 52 x 16 + 28
Step 2: Since the reminder 52 ≠ 0, we apply division lemma to 28 and 52, to get
52 = 28 x 1 + 24
Step 3: We consider the new divisor 28 and the new remainder 24, and apply the division lemma to get
28 = 24 x 1 + 4
We consider the new divisor 24 and the new remainder 4, and apply the division lemma to get
24 = 4 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 52 and 860 is 4
Notice that 4 = HCF(24,4) = HCF(28,24) = HCF(52,28) = HCF(860,52) .
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Frequently Asked Questions on HCF of 780, 676, 860 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, 676, 860?
Answer: HCF of 780, 676, 860 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 780, 676, 860 using Euclid's Algorithm?
Answer: For arbitrary numbers 780, 676, 860 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.