Highest Common Factor of 628, 133, 42, 198 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 628, 133, 42, 198 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 628, 133, 42, 198 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 628, 133, 42, 198 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 628, 133, 42, 198 is 1.
HCF(628, 133, 42, 198) = 1
HCF of 628, 133, 42, 198 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 628, 133, 42, 198 is 1.
Highest Common Factor of 628,133,42,198 is 1
Step 1: Since 628 > 133, we apply the division lemma to 628 and 133, to get
628 = 133 x 4 + 96
Step 2: Since the reminder 133 ≠ 0, we apply division lemma to 96 and 133, to get
133 = 96 x 1 + 37
Step 3: We consider the new divisor 96 and the new remainder 37, and apply the division lemma to get
96 = 37 x 2 + 22
We consider the new divisor 37 and the new remainder 22,and apply the division lemma to get
37 = 22 x 1 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 628 and 133 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(37,22) = HCF(96,37) = HCF(133,96) = HCF(628,133) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 1, we apply the division lemma to 42 and 1, to get
42 = 1 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42 is 1
Notice that 1 = HCF(42,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 198 > 1, we apply the division lemma to 198 and 1, to get
198 = 1 x 198 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 198 is 1
Notice that 1 = HCF(198,1) .
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Frequently Asked Questions on HCF of 628, 133, 42, 198 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 628, 133, 42, 198?
Answer: HCF of 628, 133, 42, 198 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 628, 133, 42, 198 using Euclid's Algorithm?
Answer: For arbitrary numbers 628, 133, 42, 198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.