Highest Common Factor of 785, 540, 878 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 785, 540, 878 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 785, 540, 878 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 785, 540, 878 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 785, 540, 878 is 1.
HCF(785, 540, 878) = 1
HCF of 785, 540, 878 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 785, 540, 878 is 1.
Highest Common Factor of 785,540,878 is 1
Step 1: Since 785 > 540, we apply the division lemma to 785 and 540, to get
785 = 540 x 1 + 245
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 245 and 540, to get
540 = 245 x 2 + 50
Step 3: We consider the new divisor 245 and the new remainder 50, and apply the division lemma to get
245 = 50 x 4 + 45
We consider the new divisor 50 and the new remainder 45,and apply the division lemma to get
50 = 45 x 1 + 5
We consider the new divisor 45 and the new remainder 5,and apply the division lemma to get
45 = 5 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 785 and 540 is 5
Notice that 5 = HCF(45,5) = HCF(50,45) = HCF(245,50) = HCF(540,245) = HCF(785,540) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 878 > 5, we apply the division lemma to 878 and 5, to get
878 = 5 x 175 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
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 5 and 878 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(878,5) .
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Frequently Asked Questions on HCF of 785, 540, 878 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 785, 540, 878?
Answer: HCF of 785, 540, 878 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 785, 540, 878 using Euclid's Algorithm?
Answer: For arbitrary numbers 785, 540, 878 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.