Highest Common Factor of 658, 940, 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 658, 940, 378 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 658, 940, 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 658, 940, 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 658, 940, 378 is 2.
HCF(658, 940, 378) = 2
HCF of 658, 940, 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 658, 940, 378 is 2.
Highest Common Factor of 658,940,378 is 2
Step 1: Since 940 > 658, we apply the division lemma to 940 and 658, to get
940 = 658 x 1 + 282
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 282 and 658, to get
658 = 282 x 2 + 94
Step 3: We consider the new divisor 282 and the new remainder 94, and apply the division lemma to get
282 = 94 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 94, the HCF of 658 and 940 is 94
Notice that 94 = HCF(282,94) = HCF(658,282) = HCF(940,658) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 378 > 94, we apply the division lemma to 378 and 94, to get
378 = 94 x 4 + 2
Step 2: Since the reminder 94 ≠ 0, we apply division lemma to 2 and 94, to get
94 = 2 x 47 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 94 and 378 is 2
Notice that 2 = HCF(94,2) = HCF(378,94) .
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Frequently Asked Questions on HCF of 658, 940, 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 658, 940, 378?
Answer: HCF of 658, 940, 378 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 658, 940, 378 using Euclid's Algorithm?
Answer: For arbitrary numbers 658, 940, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.