Highest Common Factor of 775, 915, 343 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 775, 915, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 775, 915, 343 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 775, 915, 343 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 775, 915, 343 is 1.
HCF(775, 915, 343) = 1
HCF of 775, 915, 343 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 775, 915, 343 is 1.
Highest Common Factor of 775,915,343 is 1
Step 1: Since 915 > 775, we apply the division lemma to 915 and 775, to get
915 = 775 x 1 + 140
Step 2: Since the reminder 775 ≠ 0, we apply division lemma to 140 and 775, to get
775 = 140 x 5 + 75
Step 3: We consider the new divisor 140 and the new remainder 75, and apply the division lemma to get
140 = 75 x 1 + 65
We consider the new divisor 75 and the new remainder 65,and apply the division lemma to get
75 = 65 x 1 + 10
We consider the new divisor 65 and the new remainder 10,and apply the division lemma to get
65 = 10 x 6 + 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 775 and 915 is 5
Notice that 5 = HCF(10,5) = HCF(65,10) = HCF(75,65) = HCF(140,75) = HCF(775,140) = HCF(915,775) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 343 > 5, we apply the division lemma to 343 and 5, to get
343 = 5 x 68 + 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 343 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(343,5) .
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Frequently Asked Questions on HCF of 775, 915, 343 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 775, 915, 343?
Answer: HCF of 775, 915, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 775, 915, 343 using Euclid's Algorithm?
Answer: For arbitrary numbers 775, 915, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.