Highest Common Factor of 830, 705, 763 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 830, 705, 763 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 830, 705, 763 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 830, 705, 763 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 830, 705, 763 is 1.
HCF(830, 705, 763) = 1
HCF of 830, 705, 763 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 830, 705, 763 is 1.
Highest Common Factor of 830,705,763 is 1
Step 1: Since 830 > 705, we apply the division lemma to 830 and 705, to get
830 = 705 x 1 + 125
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 125 and 705, to get
705 = 125 x 5 + 80
Step 3: We consider the new divisor 125 and the new remainder 80, and apply the division lemma to get
125 = 80 x 1 + 45
We consider the new divisor 80 and the new remainder 45,and apply the division lemma to get
80 = 45 x 1 + 35
We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get
45 = 35 x 1 + 10
We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get
35 = 10 x 3 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 830 and 705 is 5
Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(80,45) = HCF(125,80) = HCF(705,125) = HCF(830,705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 763 > 5, we apply the division lemma to 763 and 5, to get
763 = 5 x 152 + 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 763 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(763,5) .
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Frequently Asked Questions on HCF of 830, 705, 763 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 830, 705, 763?
Answer: HCF of 830, 705, 763 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 830, 705, 763 using Euclid's Algorithm?
Answer: For arbitrary numbers 830, 705, 763 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.