Highest Common Factor of 294, 759 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, 759 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 294, 759 is 3 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, 759 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, 759 is 3.
HCF(294, 759) = 3
HCF of 294, 759 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, 759 is 3.
Highest Common Factor of 294,759 is 3
Step 1: Since 759 > 294, we apply the division lemma to 759 and 294, to get
759 = 294 x 2 + 171
Step 2: Since the reminder 294 ≠ 0, we apply division lemma to 171 and 294, to get
294 = 171 x 1 + 123
Step 3: We consider the new divisor 171 and the new remainder 123, and apply the division lemma to get
171 = 123 x 1 + 48
We consider the new divisor 123 and the new remainder 48,and apply the division lemma to get
123 = 48 x 2 + 27
We consider the new divisor 48 and the new remainder 27,and apply the division lemma to get
48 = 27 x 1 + 21
We consider the new divisor 27 and the new remainder 21,and apply the division lemma to get
27 = 21 x 1 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 294 and 759 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(48,27) = HCF(123,48) = HCF(171,123) = HCF(294,171) = HCF(759,294) .
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Frequently Asked Questions on HCF of 294, 759 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, 759?
Answer: HCF of 294, 759 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 294, 759 using Euclid's Algorithm?
Answer: For arbitrary numbers 294, 759 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.