Highest Common Factor of 784, 872, 172 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 784, 872, 172 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 784, 872, 172 is 4 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 784, 872, 172 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 784, 872, 172 is 4.
HCF(784, 872, 172) = 4
HCF of 784, 872, 172 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 784, 872, 172 is 4.
Highest Common Factor of 784,872,172 is 4
Step 1: Since 872 > 784, we apply the division lemma to 872 and 784, to get
872 = 784 x 1 + 88
Step 2: Since the reminder 784 ≠ 0, we apply division lemma to 88 and 784, to get
784 = 88 x 8 + 80
Step 3: We consider the new divisor 88 and the new remainder 80, and apply the division lemma to get
88 = 80 x 1 + 8
We consider the new divisor 80 and the new remainder 8, and apply the division lemma to get
80 = 8 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 784 and 872 is 8
Notice that 8 = HCF(80,8) = HCF(88,80) = HCF(784,88) = HCF(872,784) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 172 > 8, we apply the division lemma to 172 and 8, to get
172 = 8 x 21 + 4
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 4 and 8, to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8 and 172 is 4
Notice that 4 = HCF(8,4) = HCF(172,8) .
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Frequently Asked Questions on HCF of 784, 872, 172 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 784, 872, 172?
Answer: HCF of 784, 872, 172 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 784, 872, 172 using Euclid's Algorithm?
Answer: For arbitrary numbers 784, 872, 172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.