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, 371, 194 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 628, 371, 194 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, 371, 194 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, 371, 194 is 1.
HCF(628, 371, 194) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 628, 371, 194 is 1.
Step 1: Since 628 > 371, we apply the division lemma to 628 and 371, to get
628 = 371 x 1 + 257
Step 2: Since the reminder 371 ≠ 0, we apply division lemma to 257 and 371, to get
371 = 257 x 1 + 114
Step 3: We consider the new divisor 257 and the new remainder 114, and apply the division lemma to get
257 = 114 x 2 + 29
We consider the new divisor 114 and the new remainder 29,and apply the division lemma to get
114 = 29 x 3 + 27
We consider the new divisor 29 and the new remainder 27,and apply the division lemma to get
29 = 27 x 1 + 2
We consider the new divisor 27 and the new remainder 2,and apply the division lemma to get
27 = 2 x 13 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 628 and 371 is 1
Notice that 1 = HCF(2,1) = HCF(27,2) = HCF(29,27) = HCF(114,29) = HCF(257,114) = HCF(371,257) = HCF(628,371) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 194 > 1, we apply the division lemma to 194 and 1, to get
194 = 1 x 194 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 194 is 1
Notice that 1 = HCF(194,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 371, 194?
Answer: HCF of 628, 371, 194 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 628, 371, 194 using Euclid's Algorithm?
Answer: For arbitrary numbers 628, 371, 194 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.