Highest Common Factor of 669, 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 669, 378 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 669, 378 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 669, 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 669, 378 is 3.
HCF(669, 378) = 3
HCF of 669, 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 669, 378 is 3.
Highest Common Factor of 669,378 is 3
Step 1: Since 669 > 378, we apply the division lemma to 669 and 378, to get
669 = 378 x 1 + 291
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 291 and 378, to get
378 = 291 x 1 + 87
Step 3: We consider the new divisor 291 and the new remainder 87, and apply the division lemma to get
291 = 87 x 3 + 30
We consider the new divisor 87 and the new remainder 30,and apply the division lemma to get
87 = 30 x 2 + 27
We consider the new divisor 30 and the new remainder 27,and apply the division lemma to get
30 = 27 x 1 + 3
We consider the new divisor 27 and the new remainder 3,and apply the division lemma to get
27 = 3 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 669 and 378 is 3
Notice that 3 = HCF(27,3) = HCF(30,27) = HCF(87,30) = HCF(291,87) = HCF(378,291) = HCF(669,378) .
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Frequently Asked Questions on HCF of 669, 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 669, 378?
Answer: HCF of 669, 378 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 669, 378 using Euclid's Algorithm?
Answer: For arbitrary numbers 669, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.