Highest Common Factor of 724, 977, 190 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 724, 977, 190 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 724, 977, 190 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 724, 977, 190 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 724, 977, 190 is 1.
HCF(724, 977, 190) = 1
HCF of 724, 977, 190 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 724, 977, 190 is 1.
Highest Common Factor of 724,977,190 is 1
Step 1: Since 977 > 724, we apply the division lemma to 977 and 724, to get
977 = 724 x 1 + 253
Step 2: Since the reminder 724 ≠ 0, we apply division lemma to 253 and 724, to get
724 = 253 x 2 + 218
Step 3: We consider the new divisor 253 and the new remainder 218, and apply the division lemma to get
253 = 218 x 1 + 35
We consider the new divisor 218 and the new remainder 35,and apply the division lemma to get
218 = 35 x 6 + 8
We consider the new divisor 35 and the new remainder 8,and apply the division lemma to get
35 = 8 x 4 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 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 724 and 977 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(35,8) = HCF(218,35) = HCF(253,218) = HCF(724,253) = HCF(977,724) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 190 > 1, we apply the division lemma to 190 and 1, to get
190 = 1 x 190 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 190 is 1
Notice that 1 = HCF(190,1) .
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Frequently Asked Questions on HCF of 724, 977, 190 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 724, 977, 190?
Answer: HCF of 724, 977, 190 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 724, 977, 190 using Euclid's Algorithm?
Answer: For arbitrary numbers 724, 977, 190 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
