Highest Common Factor of 103, 698, 303 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 103, 698, 303 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 103, 698, 303 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 103, 698, 303 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 103, 698, 303 is 1.
HCF(103, 698, 303) = 1
HCF of 103, 698, 303 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 103, 698, 303 is 1.
Highest Common Factor of 103,698,303 is 1
Step 1: Since 698 > 103, we apply the division lemma to 698 and 103, to get
698 = 103 x 6 + 80
Step 2: Since the reminder 103 ≠ 0, we apply division lemma to 80 and 103, to get
103 = 80 x 1 + 23
Step 3: We consider the new divisor 80 and the new remainder 23, and apply the division lemma to get
80 = 23 x 3 + 11
We consider the new divisor 23 and the new remainder 11,and apply the division lemma to get
23 = 11 x 2 + 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 103 and 698 is 1
Notice that 1 = HCF(11,1) = HCF(23,11) = HCF(80,23) = HCF(103,80) = HCF(698,103) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 303 > 1, we apply the division lemma to 303 and 1, to get
303 = 1 x 303 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 303 is 1
Notice that 1 = HCF(303,1) .
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Frequently Asked Questions on HCF of 103, 698, 303 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 103, 698, 303?
Answer: HCF of 103, 698, 303 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 103, 698, 303 using Euclid's Algorithm?
Answer: For arbitrary numbers 103, 698, 303 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.