Highest Common Factor of 312, 677, 355, 80 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 312, 677, 355, 80 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 677, 355, 80 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 312, 677, 355, 80 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 312, 677, 355, 80 is 1.
HCF(312, 677, 355, 80) = 1
HCF of 312, 677, 355, 80 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 677, 355, 80 is 1.
Highest Common Factor of 312,677,355,80 is 1
Step 1: Since 677 > 312, we apply the division lemma to 677 and 312, to get
677 = 312 x 2 + 53
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 53 and 312, to get
312 = 53 x 5 + 47
Step 3: We consider the new divisor 53 and the new remainder 47, and apply the division lemma to get
53 = 47 x 1 + 6
We consider the new divisor 47 and the new remainder 6,and apply the division lemma to get
47 = 6 x 7 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 312 and 677 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(47,6) = HCF(53,47) = HCF(312,53) = HCF(677,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 355 > 1, we apply the division lemma to 355 and 1, to get
355 = 1 x 355 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 355 is 1
Notice that 1 = HCF(355,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 80 > 1, we apply the division lemma to 80 and 1, to get
80 = 1 x 80 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 80 is 1
Notice that 1 = HCF(80,1) .
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Frequently Asked Questions on HCF of 312, 677, 355, 80 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 312, 677, 355, 80?
Answer: HCF of 312, 677, 355, 80 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 677, 355, 80 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 677, 355, 80 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.