Highest Common Factor of 172, 332, 684 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 172, 332, 684 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 172, 332, 684 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 172, 332, 684 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 172, 332, 684 is 4.
HCF(172, 332, 684) = 4
HCF of 172, 332, 684 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 172, 332, 684 is 4.
Highest Common Factor of 172,332,684 is 4
Step 1: Since 332 > 172, we apply the division lemma to 332 and 172, to get
332 = 172 x 1 + 160
Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 160 and 172, to get
172 = 160 x 1 + 12
Step 3: We consider the new divisor 160 and the new remainder 12, and apply the division lemma to get
160 = 12 x 13 + 4
We consider the new divisor 12 and the new remainder 4, and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 172 and 332 is 4
Notice that 4 = HCF(12,4) = HCF(160,12) = HCF(172,160) = HCF(332,172) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 684 > 4, we apply the division lemma to 684 and 4, to get
684 = 4 x 171 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 684 is 4
Notice that 4 = HCF(684,4) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 172, 332, 684 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 172, 332, 684?
Answer: HCF of 172, 332, 684 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 172, 332, 684 using Euclid's Algorithm?
Answer: For arbitrary numbers 172, 332, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.