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, 868, 472 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 126, 868, 472 is 2 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, 868, 472 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, 868, 472 is 2.
HCF(126, 868, 472) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 126, 868, 472 is 2.
Step 1: Since 868 > 126, we apply the division lemma to 868 and 126, to get
868 = 126 x 6 + 112
Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 112 and 126, to get
126 = 112 x 1 + 14
Step 3: We consider the new divisor 112 and the new remainder 14, and apply the division lemma to get
112 = 14 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 126 and 868 is 14
Notice that 14 = HCF(112,14) = HCF(126,112) = HCF(868,126) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 472 > 14, we apply the division lemma to 472 and 14, to get
472 = 14 x 33 + 10
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 10 and 14, to get
14 = 10 x 1 + 4
Step 3: 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 14 and 472 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(472,14) .
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, 868, 472?
Answer: HCF of 126, 868, 472 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 126, 868, 472 using Euclid's Algorithm?
Answer: For arbitrary numbers 126, 868, 472 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.