Highest Common Factor of 563, 208, 74, 174 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 563, 208, 74, 174 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 563, 208, 74, 174 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 563, 208, 74, 174 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 563, 208, 74, 174 is 1.
HCF(563, 208, 74, 174) = 1
HCF of 563, 208, 74, 174 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 563, 208, 74, 174 is 1.
Highest Common Factor of 563,208,74,174 is 1
Step 1: Since 563 > 208, we apply the division lemma to 563 and 208, to get
563 = 208 x 2 + 147
Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 147 and 208, to get
208 = 147 x 1 + 61
Step 3: We consider the new divisor 147 and the new remainder 61, and apply the division lemma to get
147 = 61 x 2 + 25
We consider the new divisor 61 and the new remainder 25,and apply the division lemma to get
61 = 25 x 2 + 11
We consider the new divisor 25 and the new remainder 11,and apply the division lemma to get
25 = 11 x 2 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
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 563 and 208 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(25,11) = HCF(61,25) = HCF(147,61) = HCF(208,147) = HCF(563,208) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 1, we apply the division lemma to 74 and 1, to get
74 = 1 x 74 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 74 is 1
Notice that 1 = HCF(74,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 174 > 1, we apply the division lemma to 174 and 1, to get
174 = 1 x 174 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 174 is 1
Notice that 1 = HCF(174,1) .
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Frequently Asked Questions on HCF of 563, 208, 74, 174 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 563, 208, 74, 174?
Answer: HCF of 563, 208, 74, 174 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 563, 208, 74, 174 using Euclid's Algorithm?
Answer: For arbitrary numbers 563, 208, 74, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
