Highest Common Factor of 378, 624, 298, 682 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, 624, 298, 682 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 624, 298, 682 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, 624, 298, 682 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, 624, 298, 682 is 2.
HCF(378, 624, 298, 682) = 2
HCF of 378, 624, 298, 682 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, 624, 298, 682 is 2.
Highest Common Factor of 378,624,298,682 is 2
Step 1: Since 624 > 378, we apply the division lemma to 624 and 378, to get
624 = 378 x 1 + 246
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 246 and 378, to get
378 = 246 x 1 + 132
Step 3: We consider the new divisor 246 and the new remainder 132, and apply the division lemma to get
246 = 132 x 1 + 114
We consider the new divisor 132 and the new remainder 114,and apply the division lemma to get
132 = 114 x 1 + 18
We consider the new divisor 114 and the new remainder 18,and apply the division lemma to get
114 = 18 x 6 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 378 and 624 is 6
Notice that 6 = HCF(18,6) = HCF(114,18) = HCF(132,114) = HCF(246,132) = HCF(378,246) = HCF(624,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 298 > 6, we apply the division lemma to 298 and 6, to get
298 = 6 x 49 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 298 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(298,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 682 > 2, we apply the division lemma to 682 and 2, to get
682 = 2 x 341 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 682 is 2
Notice that 2 = HCF(682,2) .
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Frequently Asked Questions on HCF of 378, 624, 298, 682 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, 624, 298, 682?
Answer: HCF of 378, 624, 298, 682 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 624, 298, 682 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 624, 298, 682 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.