Highest Common Factor of 364, 754, 378 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, 754, 378 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 364, 754, 378 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, 754, 378 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, 754, 378 is 2.
HCF(364, 754, 378) = 2
HCF of 364, 754, 378 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, 754, 378 is 2.
Highest Common Factor of 364,754,378 is 2
Step 1: Since 754 > 364, we apply the division lemma to 754 and 364, to get
754 = 364 x 2 + 26
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 26 and 364, to get
364 = 26 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 364 and 754 is 26
Notice that 26 = HCF(364,26) = HCF(754,364) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 378 > 26, we apply the division lemma to 378 and 26, to get
378 = 26 x 14 + 14
Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 14 and 26, to get
26 = 14 x 1 + 12
Step 3: We consider the new divisor 14 and the new remainder 12, and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2, and apply the division lemma 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 378 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(378,26) .
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Frequently Asked Questions on HCF of 364, 754, 378 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, 754, 378?
Answer: HCF of 364, 754, 378 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 364, 754, 378 using Euclid's Algorithm?
Answer: For arbitrary numbers 364, 754, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
