Highest Common Factor of 364, 494, 12 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 364, 494, 12 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 364, 494, 12 is 2 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 364, 494, 12 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 364, 494, 12 is 2.
HCF(364, 494, 12) = 2
HCF of 364, 494, 12 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 364, 494, 12 is 2.
Highest Common Factor of 364,494,12 is 2
Step 1: Since 494 > 364, we apply the division lemma to 494 and 364, to get
494 = 364 x 1 + 130
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 130 and 364, to get
364 = 130 x 2 + 104
Step 3: We consider the new divisor 130 and the new remainder 104, and apply the division lemma to get
130 = 104 x 1 + 26
We consider the new divisor 104 and the new remainder 26, and apply the division lemma to get
104 = 26 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 364 and 494 is 26
Notice that 26 = HCF(104,26) = HCF(130,104) = HCF(364,130) = HCF(494,364) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 26 > 12, we apply the division lemma to 26 and 12, to get
26 = 12 x 2 + 2
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 2 and 12, to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 26 and 12 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) .
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Frequently Asked Questions on HCF of 364, 494, 12 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 364, 494, 12?
Answer: HCF of 364, 494, 12 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 364, 494, 12 using Euclid's Algorithm?
Answer: For arbitrary numbers 364, 494, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.