Highest Common Factor of 624, 390, 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 624, 390, 378 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 624, 390, 378 is 6 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 624, 390, 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 624, 390, 378 is 6.
HCF(624, 390, 378) = 6
HCF of 624, 390, 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 624, 390, 378 is 6.
Highest Common Factor of 624,390,378 is 6
Step 1: Since 624 > 390, we apply the division lemma to 624 and 390, to get
624 = 390 x 1 + 234
Step 2: Since the reminder 390 ≠ 0, we apply division lemma to 234 and 390, to get
390 = 234 x 1 + 156
Step 3: We consider the new divisor 234 and the new remainder 156, and apply the division lemma to get
234 = 156 x 1 + 78
We consider the new divisor 156 and the new remainder 78, and apply the division lemma to get
156 = 78 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 78, the HCF of 624 and 390 is 78
Notice that 78 = HCF(156,78) = HCF(234,156) = HCF(390,234) = HCF(624,390) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 378 > 78, we apply the division lemma to 378 and 78, to get
378 = 78 x 4 + 66
Step 2: Since the reminder 78 ≠ 0, we apply division lemma to 66 and 78, to get
78 = 66 x 1 + 12
Step 3: We consider the new divisor 66 and the new remainder 12, and apply the division lemma to get
66 = 12 x 5 + 6
We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 78 and 378 is 6
Notice that 6 = HCF(12,6) = HCF(66,12) = HCF(78,66) = HCF(378,78) .
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Frequently Asked Questions on HCF of 624, 390, 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 624, 390, 378?
Answer: HCF of 624, 390, 378 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 624, 390, 378 using Euclid's Algorithm?
Answer: For arbitrary numbers 624, 390, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
