Highest Common Factor of 107, 136, 174, 60 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 107, 136, 174, 60 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 107, 136, 174, 60 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 107, 136, 174, 60 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 107, 136, 174, 60 is 1.
HCF(107, 136, 174, 60) = 1
HCF of 107, 136, 174, 60 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 107, 136, 174, 60 is 1.
Highest Common Factor of 107,136,174,60 is 1
Step 1: Since 136 > 107, we apply the division lemma to 136 and 107, to get
136 = 107 x 1 + 29
Step 2: Since the reminder 107 ≠ 0, we apply division lemma to 29 and 107, to get
107 = 29 x 3 + 20
Step 3: We consider the new divisor 29 and the new remainder 20, and apply the division lemma to get
29 = 20 x 1 + 9
We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get
20 = 9 x 2 + 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 107 and 136 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(29,20) = HCF(107,29) = HCF(136,107) .
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) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60 > 1, we apply the division lemma to 60 and 1, to get
60 = 1 x 60 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 60 is 1
Notice that 1 = HCF(60,1) .
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Frequently Asked Questions on HCF of 107, 136, 174, 60 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 107, 136, 174, 60?
Answer: HCF of 107, 136, 174, 60 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 107, 136, 174, 60 using Euclid's Algorithm?
Answer: For arbitrary numbers 107, 136, 174, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.