Highest Common Factor of 123, 8074, 8803 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 123, 8074, 8803 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 123, 8074, 8803 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 123, 8074, 8803 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 123, 8074, 8803 is 1.
HCF(123, 8074, 8803) = 1
HCF of 123, 8074, 8803 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 123, 8074, 8803 is 1.
Highest Common Factor of 123,8074,8803 is 1
Step 1: Since 8074 > 123, we apply the division lemma to 8074 and 123, to get
8074 = 123 x 65 + 79
Step 2: Since the reminder 123 ≠ 0, we apply division lemma to 79 and 123, to get
123 = 79 x 1 + 44
Step 3: We consider the new divisor 79 and the new remainder 44, and apply the division lemma to get
79 = 44 x 1 + 35
We consider the new divisor 44 and the new remainder 35,and apply the division lemma to get
44 = 35 x 1 + 9
We consider the new divisor 35 and the new remainder 9,and apply the division lemma to get
35 = 9 x 3 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 123 and 8074 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(35,9) = HCF(44,35) = HCF(79,44) = HCF(123,79) = HCF(8074,123) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8803 > 1, we apply the division lemma to 8803 and 1, to get
8803 = 1 x 8803 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8803 is 1
Notice that 1 = HCF(8803,1) .
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Frequently Asked Questions on HCF of 123, 8074, 8803 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 123, 8074, 8803?
Answer: HCF of 123, 8074, 8803 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 123, 8074, 8803 using Euclid's Algorithm?
Answer: For arbitrary numbers 123, 8074, 8803 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.