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 126, 974, 831 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 126, 974, 831 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 126, 974, 831 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 126, 974, 831 is 1.
HCF(126, 974, 831) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 126, 974, 831 is 1.
Step 1: Since 974 > 126, we apply the division lemma to 974 and 126, to get
974 = 126 x 7 + 92
Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 92 and 126, to get
126 = 92 x 1 + 34
Step 3: We consider the new divisor 92 and the new remainder 34, and apply the division lemma to get
92 = 34 x 2 + 24
We consider the new divisor 34 and the new remainder 24,and apply the division lemma to get
34 = 24 x 1 + 10
We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get
24 = 10 x 2 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 126 and 974 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(34,24) = HCF(92,34) = HCF(126,92) = HCF(974,126) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 831 > 2, we apply the division lemma to 831 and 2, to get
831 = 2 x 415 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 831 is 1
Notice that 1 = HCF(2,1) = HCF(831,2) .
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 126, 974, 831?
Answer: HCF of 126, 974, 831 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 126, 974, 831 using Euclid's Algorithm?
Answer: For arbitrary numbers 126, 974, 831 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.