Highest Common Factor of 319, 868, 123 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 319, 868, 123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 319, 868, 123 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 319, 868, 123 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 319, 868, 123 is 1.
HCF(319, 868, 123) = 1
HCF of 319, 868, 123 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 319, 868, 123 is 1.
Highest Common Factor of 319,868,123 is 1
Step 1: Since 868 > 319, we apply the division lemma to 868 and 319, to get
868 = 319 x 2 + 230
Step 2: Since the reminder 319 ≠ 0, we apply division lemma to 230 and 319, to get
319 = 230 x 1 + 89
Step 3: We consider the new divisor 230 and the new remainder 89, and apply the division lemma to get
230 = 89 x 2 + 52
We consider the new divisor 89 and the new remainder 52,and apply the division lemma to get
89 = 52 x 1 + 37
We consider the new divisor 52 and the new remainder 37,and apply the division lemma to get
52 = 37 x 1 + 15
We consider the new divisor 37 and the new remainder 15,and apply the division lemma to get
37 = 15 x 2 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 319 and 868 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(37,15) = HCF(52,37) = HCF(89,52) = HCF(230,89) = HCF(319,230) = HCF(868,319) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 123 > 1, we apply the division lemma to 123 and 1, to get
123 = 1 x 123 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 123 is 1
Notice that 1 = HCF(123,1) .
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Frequently Asked Questions on HCF of 319, 868, 123 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 319, 868, 123?
Answer: HCF of 319, 868, 123 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 319, 868, 123 using Euclid's Algorithm?
Answer: For arbitrary numbers 319, 868, 123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.