Highest Common Factor of 378, 973, 43 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, 973, 43 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 973, 43 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, 973, 43 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, 973, 43 is 1.
HCF(378, 973, 43) = 1
HCF of 378, 973, 43 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, 973, 43 is 1.
Highest Common Factor of 378,973,43 is 1
Step 1: Since 973 > 378, we apply the division lemma to 973 and 378, to get
973 = 378 x 2 + 217
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 217 and 378, to get
378 = 217 x 1 + 161
Step 3: We consider the new divisor 217 and the new remainder 161, and apply the division lemma to get
217 = 161 x 1 + 56
We consider the new divisor 161 and the new remainder 56,and apply the division lemma to get
161 = 56 x 2 + 49
We consider the new divisor 56 and the new remainder 49,and apply the division lemma to get
56 = 49 x 1 + 7
We consider the new divisor 49 and the new remainder 7,and apply the division lemma to get
49 = 7 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 378 and 973 is 7
Notice that 7 = HCF(49,7) = HCF(56,49) = HCF(161,56) = HCF(217,161) = HCF(378,217) = HCF(973,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 43 > 7, we apply the division lemma to 43 and 7, to get
43 = 7 x 6 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 43 is 1
Notice that 1 = HCF(7,1) = HCF(43,7) .
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Frequently Asked Questions on HCF of 378, 973, 43 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, 973, 43?
Answer: HCF of 378, 973, 43 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 973, 43 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 973, 43 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.