Highest Common Factor of 997, 719, 374 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 997, 719, 374 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 997, 719, 374 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 997, 719, 374 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 997, 719, 374 is 1.
HCF(997, 719, 374) = 1
HCF of 997, 719, 374 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 997, 719, 374 is 1.
Highest Common Factor of 997,719,374 is 1
Step 1: Since 997 > 719, we apply the division lemma to 997 and 719, to get
997 = 719 x 1 + 278
Step 2: Since the reminder 719 ≠ 0, we apply division lemma to 278 and 719, to get
719 = 278 x 2 + 163
Step 3: We consider the new divisor 278 and the new remainder 163, and apply the division lemma to get
278 = 163 x 1 + 115
We consider the new divisor 163 and the new remainder 115,and apply the division lemma to get
163 = 115 x 1 + 48
We consider the new divisor 115 and the new remainder 48,and apply the division lemma to get
115 = 48 x 2 + 19
We consider the new divisor 48 and the new remainder 19,and apply the division lemma to get
48 = 19 x 2 + 10
We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get
19 = 10 x 1 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 997 and 719 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(48,19) = HCF(115,48) = HCF(163,115) = HCF(278,163) = HCF(719,278) = HCF(997,719) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 374 > 1, we apply the division lemma to 374 and 1, to get
374 = 1 x 374 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 374 is 1
Notice that 1 = HCF(374,1) .
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Frequently Asked Questions on HCF of 997, 719, 374 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 997, 719, 374?
Answer: HCF of 997, 719, 374 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 997, 719, 374 using Euclid's Algorithm?
Answer: For arbitrary numbers 997, 719, 374 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.