Highest Common Factor of 378, 882, 74 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, 882, 74 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 882, 74 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 378, 882, 74 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, 882, 74 is 2.
HCF(378, 882, 74) = 2
HCF of 378, 882, 74 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, 882, 74 is 2.
Highest Common Factor of 378,882,74 is 2
Step 1: Since 882 > 378, we apply the division lemma to 882 and 378, to get
882 = 378 x 2 + 126
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 126 and 378, to get
378 = 126 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 126, the HCF of 378 and 882 is 126
Notice that 126 = HCF(378,126) = HCF(882,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 126 > 74, we apply the division lemma to 126 and 74, to get
126 = 74 x 1 + 52
Step 2: Since the reminder 74 ≠ 0, we apply division lemma to 52 and 74, to get
74 = 52 x 1 + 22
Step 3: We consider the new divisor 52 and the new remainder 22, and apply the division lemma to get
52 = 22 x 2 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 126 and 74 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(52,22) = HCF(74,52) = HCF(126,74) .
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Frequently Asked Questions on HCF of 378, 882, 74 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, 882, 74?
Answer: HCF of 378, 882, 74 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 882, 74 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 882, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.