Highest Common Factor of 378, 659 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 378, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 659 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 378, 659 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 378, 659 is 1.
HCF(378, 659) = 1
HCF of 378, 659 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 378, 659 is 1.
Highest Common Factor of 378,659 is 1
Step 1: Since 659 > 378, we apply the division lemma to 659 and 378, to get
659 = 378 x 1 + 281
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 281 and 378, to get
378 = 281 x 1 + 97
Step 3: We consider the new divisor 281 and the new remainder 97, and apply the division lemma to get
281 = 97 x 2 + 87
We consider the new divisor 97 and the new remainder 87,and apply the division lemma to get
97 = 87 x 1 + 10
We consider the new divisor 87 and the new remainder 10,and apply the division lemma to get
87 = 10 x 8 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 378 and 659 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(87,10) = HCF(97,87) = HCF(281,97) = HCF(378,281) = HCF(659,378) .
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Frequently Asked Questions on HCF of 378, 659 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 378, 659?
Answer: HCF of 378, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 659 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.