Highest Common Factor of 1298, 7709, 31204 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 1298, 7709, 31204 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1298, 7709, 31204 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 1298, 7709, 31204 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 1298, 7709, 31204 is 1.
HCF(1298, 7709, 31204) = 1
HCF of 1298, 7709, 31204 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1298, 7709, 31204 is 1.
Highest Common Factor of 1298,7709,31204 is 1
Step 1: Since 7709 > 1298, we apply the division lemma to 7709 and 1298, to get
7709 = 1298 x 5 + 1219
Step 2: Since the reminder 1298 ≠ 0, we apply division lemma to 1219 and 1298, to get
1298 = 1219 x 1 + 79
Step 3: We consider the new divisor 1219 and the new remainder 79, and apply the division lemma to get
1219 = 79 x 15 + 34
We consider the new divisor 79 and the new remainder 34,and apply the division lemma to get
79 = 34 x 2 + 11
We consider the new divisor 34 and the new remainder 11,and apply the division lemma to get
34 = 11 x 3 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1298 and 7709 is 1
Notice that 1 = HCF(11,1) = HCF(34,11) = HCF(79,34) = HCF(1219,79) = HCF(1298,1219) = HCF(7709,1298) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31204 > 1, we apply the division lemma to 31204 and 1, to get
31204 = 1 x 31204 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31204 is 1
Notice that 1 = HCF(31204,1) .
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Frequently Asked Questions on HCF of 1298, 7709, 31204 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 1298, 7709, 31204?
Answer: HCF of 1298, 7709, 31204 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1298, 7709, 31204 using Euclid's Algorithm?
Answer: For arbitrary numbers 1298, 7709, 31204 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.