Highest Common Factor of 508, 701, 160, 78 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 508, 701, 160, 78 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 508, 701, 160, 78 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 508, 701, 160, 78 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 508, 701, 160, 78 is 1.
HCF(508, 701, 160, 78) = 1
HCF of 508, 701, 160, 78 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 508, 701, 160, 78 is 1.
Highest Common Factor of 508,701,160,78 is 1
Step 1: Since 701 > 508, we apply the division lemma to 701 and 508, to get
701 = 508 x 1 + 193
Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 193 and 508, to get
508 = 193 x 2 + 122
Step 3: We consider the new divisor 193 and the new remainder 122, and apply the division lemma to get
193 = 122 x 1 + 71
We consider the new divisor 122 and the new remainder 71,and apply the division lemma to get
122 = 71 x 1 + 51
We consider the new divisor 71 and the new remainder 51,and apply the division lemma to get
71 = 51 x 1 + 20
We consider the new divisor 51 and the new remainder 20,and apply the division lemma to get
51 = 20 x 2 + 11
We consider the new divisor 20 and the new remainder 11,and apply the division lemma to get
20 = 11 x 1 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 508 and 701 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(51,20) = HCF(71,51) = HCF(122,71) = HCF(193,122) = HCF(508,193) = HCF(701,508) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 160 > 1, we apply the division lemma to 160 and 1, to get
160 = 1 x 160 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 160 is 1
Notice that 1 = HCF(160,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78 > 1, we apply the division lemma to 78 and 1, to get
78 = 1 x 78 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78 is 1
Notice that 1 = HCF(78,1) .
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Frequently Asked Questions on HCF of 508, 701, 160, 78 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 508, 701, 160, 78?
Answer: HCF of 508, 701, 160, 78 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 508, 701, 160, 78 using Euclid's Algorithm?
Answer: For arbitrary numbers 508, 701, 160, 78 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.