Highest Common Factor of 107, 772, 223, 32 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, 772, 223, 32 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 107, 772, 223, 32 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, 772, 223, 32 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, 772, 223, 32 is 1.
HCF(107, 772, 223, 32) = 1
HCF of 107, 772, 223, 32 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, 772, 223, 32 is 1.
Highest Common Factor of 107,772,223,32 is 1
Step 1: Since 772 > 107, we apply the division lemma to 772 and 107, to get
772 = 107 x 7 + 23
Step 2: Since the reminder 107 ≠ 0, we apply division lemma to 23 and 107, to get
107 = 23 x 4 + 15
Step 3: We consider the new divisor 23 and the new remainder 15, and apply the division lemma to get
23 = 15 x 1 + 8
We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get
15 = 8 x 1 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 107 and 772 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(23,15) = HCF(107,23) = HCF(772,107) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 223 > 1, we apply the division lemma to 223 and 1, to get
223 = 1 x 223 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 223 is 1
Notice that 1 = HCF(223,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 1, we apply the division lemma to 32 and 1, to get
32 = 1 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 32 is 1
Notice that 1 = HCF(32,1) .
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Frequently Asked Questions on HCF of 107, 772, 223, 32 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, 772, 223, 32?
Answer: HCF of 107, 772, 223, 32 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 107, 772, 223, 32 using Euclid's Algorithm?
Answer: For arbitrary numbers 107, 772, 223, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.