Highest Common Factor of 378, 9006 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, 9006 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 9006 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 378, 9006 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, 9006 is 6.
HCF(378, 9006) = 6
HCF of 378, 9006 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, 9006 is 6.
Highest Common Factor of 378,9006 is 6
Step 1: Since 9006 > 378, we apply the division lemma to 9006 and 378, to get
9006 = 378 x 23 + 312
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 312 and 378, to get
378 = 312 x 1 + 66
Step 3: We consider the new divisor 312 and the new remainder 66, and apply the division lemma to get
312 = 66 x 4 + 48
We consider the new divisor 66 and the new remainder 48,and apply the division lemma to get
66 = 48 x 1 + 18
We consider the new divisor 48 and the new remainder 18,and apply the division lemma to get
48 = 18 x 2 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 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 378 and 9006 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(48,18) = HCF(66,48) = HCF(312,66) = HCF(378,312) = HCF(9006,378) .
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Frequently Asked Questions on HCF of 378, 9006 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, 9006?
Answer: HCF of 378, 9006 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 9006 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 9006 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.