Highest Common Factor of 645, 198, 442 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 645, 198, 442 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 645, 198, 442 is 1 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 645, 198, 442 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 645, 198, 442 is 1.
HCF(645, 198, 442) = 1
HCF of 645, 198, 442 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 645, 198, 442 is 1.
Highest Common Factor of 645,198,442 is 1
Step 1: Since 645 > 198, we apply the division lemma to 645 and 198, to get
645 = 198 x 3 + 51
Step 2: Since the reminder 198 ≠ 0, we apply division lemma to 51 and 198, to get
198 = 51 x 3 + 45
Step 3: We consider the new divisor 51 and the new remainder 45, and apply the division lemma to get
51 = 45 x 1 + 6
We consider the new divisor 45 and the new remainder 6,and apply the division lemma to get
45 = 6 x 7 + 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 645 and 198 is 3
Notice that 3 = HCF(6,3) = HCF(45,6) = HCF(51,45) = HCF(198,51) = HCF(645,198) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 442 > 3, we apply the division lemma to 442 and 3, to get
442 = 3 x 147 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 442 is 1
Notice that 1 = HCF(3,1) = HCF(442,3) .
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Frequently Asked Questions on HCF of 645, 198, 442 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 645, 198, 442?
Answer: HCF of 645, 198, 442 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 645, 198, 442 using Euclid's Algorithm?
Answer: For arbitrary numbers 645, 198, 442 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.