Highest Common Factor of 621, 945, 102 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 621, 945, 102 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 621, 945, 102 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 621, 945, 102 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 621, 945, 102 is 3.
HCF(621, 945, 102) = 3
HCF of 621, 945, 102 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 621, 945, 102 is 3.
Highest Common Factor of 621,945,102 is 3
Step 1: Since 945 > 621, we apply the division lemma to 945 and 621, to get
945 = 621 x 1 + 324
Step 2: Since the reminder 621 ≠ 0, we apply division lemma to 324 and 621, to get
621 = 324 x 1 + 297
Step 3: We consider the new divisor 324 and the new remainder 297, and apply the division lemma to get
324 = 297 x 1 + 27
We consider the new divisor 297 and the new remainder 27, and apply the division lemma to get
297 = 27 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 621 and 945 is 27
Notice that 27 = HCF(297,27) = HCF(324,297) = HCF(621,324) = HCF(945,621) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 102 > 27, we apply the division lemma to 102 and 27, to get
102 = 27 x 3 + 21
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 21 and 27, to get
27 = 21 x 1 + 6
Step 3: We consider the new divisor 21 and the new remainder 6, and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 27 and 102 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(102,27) .
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Frequently Asked Questions on HCF of 621, 945, 102 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 621, 945, 102?
Answer: HCF of 621, 945, 102 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 621, 945, 102 using Euclid's Algorithm?
Answer: For arbitrary numbers 621, 945, 102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.