Highest Common Factor of 294, 210, 319 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 294, 210, 319 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 294, 210, 319 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 294, 210, 319 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 294, 210, 319 is 1.
HCF(294, 210, 319) = 1
HCF of 294, 210, 319 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 294, 210, 319 is 1.
Highest Common Factor of 294,210,319 is 1
Step 1: Since 294 > 210, we apply the division lemma to 294 and 210, to get
294 = 210 x 1 + 84
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 84 and 210, to get
210 = 84 x 2 + 42
Step 3: We consider the new divisor 84 and the new remainder 42, and apply the division lemma to get
84 = 42 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 294 and 210 is 42
Notice that 42 = HCF(84,42) = HCF(210,84) = HCF(294,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 319 > 42, we apply the division lemma to 319 and 42, to get
319 = 42 x 7 + 25
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 25 and 42, to get
42 = 25 x 1 + 17
Step 3: We consider the new divisor 25 and the new remainder 17, and apply the division lemma to get
25 = 17 x 1 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 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 42 and 319 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(25,17) = HCF(42,25) = HCF(319,42) .
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Frequently Asked Questions on HCF of 294, 210, 319 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 294, 210, 319?
Answer: HCF of 294, 210, 319 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 294, 210, 319 using Euclid's Algorithm?
Answer: For arbitrary numbers 294, 210, 319 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.