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 637, 962, 194 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 637, 962, 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 637, 962, 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 637, 962, 194 is 1.
HCF(637, 962, 194) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 637, 962, 194 is 1.
Step 1: Since 962 > 637, we apply the division lemma to 962 and 637, to get
962 = 637 x 1 + 325
Step 2: Since the reminder 637 ≠ 0, we apply division lemma to 325 and 637, to get
637 = 325 x 1 + 312
Step 3: We consider the new divisor 325 and the new remainder 312, and apply the division lemma to get
325 = 312 x 1 + 13
We consider the new divisor 312 and the new remainder 13, and apply the division lemma to get
312 = 13 x 24 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 637 and 962 is 13
Notice that 13 = HCF(312,13) = HCF(325,312) = HCF(637,325) = HCF(962,637) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 194 > 13, we apply the division lemma to 194 and 13, to get
194 = 13 x 14 + 12
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 12 and 13, to get
13 = 12 x 1 + 1
Step 3: We consider the new divisor 12 and the new remainder 1, and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 194 is 1
Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(194,13) .
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 637, 962, 194?
Answer: HCF of 637, 962, 194 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 637, 962, 194 using Euclid's Algorithm?
Answer: For arbitrary numbers 637, 962, 194 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.