Highest Common Factor of 651, 378, 390 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 651, 378, 390 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 651, 378, 390 is 3 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 651, 378, 390 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 651, 378, 390 is 3.
HCF(651, 378, 390) = 3
HCF of 651, 378, 390 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 651, 378, 390 is 3.
Highest Common Factor of 651,378,390 is 3
Step 1: Since 651 > 378, we apply the division lemma to 651 and 378, to get
651 = 378 x 1 + 273
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 273 and 378, to get
378 = 273 x 1 + 105
Step 3: We consider the new divisor 273 and the new remainder 105, and apply the division lemma to get
273 = 105 x 2 + 63
We consider the new divisor 105 and the new remainder 63,and apply the division lemma to get
105 = 63 x 1 + 42
We consider the new divisor 63 and the new remainder 42,and apply the division lemma to get
63 = 42 x 1 + 21
We consider the new divisor 42 and the new remainder 21,and apply the division lemma to get
42 = 21 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 651 and 378 is 21
Notice that 21 = HCF(42,21) = HCF(63,42) = HCF(105,63) = HCF(273,105) = HCF(378,273) = HCF(651,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 390 > 21, we apply the division lemma to 390 and 21, to get
390 = 21 x 18 + 12
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 12 and 21, to get
21 = 12 x 1 + 9
Step 3: We consider the new divisor 12 and the new remainder 9, and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 21 and 390 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(390,21) .
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Frequently Asked Questions on HCF of 651, 378, 390 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 651, 378, 390?
Answer: HCF of 651, 378, 390 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 651, 378, 390 using Euclid's Algorithm?
Answer: For arbitrary numbers 651, 378, 390 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.