Highest Common Factor of 378, 891, 447 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, 891, 447 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 891, 447 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 378, 891, 447 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, 891, 447 is 3.
HCF(378, 891, 447) = 3
HCF of 378, 891, 447 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, 891, 447 is 3.
Highest Common Factor of 378,891,447 is 3
Step 1: Since 891 > 378, we apply the division lemma to 891 and 378, to get
891 = 378 x 2 + 135
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 135 and 378, to get
378 = 135 x 2 + 108
Step 3: We consider the new divisor 135 and the new remainder 108, and apply the division lemma to get
135 = 108 x 1 + 27
We consider the new divisor 108 and the new remainder 27, and apply the division lemma to get
108 = 27 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 378 and 891 is 27
Notice that 27 = HCF(108,27) = HCF(135,108) = HCF(378,135) = HCF(891,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 447 > 27, we apply the division lemma to 447 and 27, to get
447 = 27 x 16 + 15
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 15 and 27, to get
27 = 15 x 1 + 12
Step 3: We consider the new divisor 15 and the new remainder 12, and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 27 and 447 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(447,27) .
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Frequently Asked Questions on HCF of 378, 891, 447 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, 891, 447?
Answer: HCF of 378, 891, 447 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 891, 447 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 891, 447 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.