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 984, 705, 172 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 984, 705, 172 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 984, 705, 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 984, 705, 172 is 1.
HCF(984, 705, 172) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 984, 705, 172 is 1.
Step 1: Since 984 > 705, we apply the division lemma to 984 and 705, to get
984 = 705 x 1 + 279
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 279 and 705, to get
705 = 279 x 2 + 147
Step 3: We consider the new divisor 279 and the new remainder 147, and apply the division lemma to get
279 = 147 x 1 + 132
We consider the new divisor 147 and the new remainder 132,and apply the division lemma to get
147 = 132 x 1 + 15
We consider the new divisor 132 and the new remainder 15,and apply the division lemma to get
132 = 15 x 8 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 984 and 705 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(132,15) = HCF(147,132) = HCF(279,147) = HCF(705,279) = HCF(984,705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 172 > 3, we apply the division lemma to 172 and 3, to get
172 = 3 x 57 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 172 is 1
Notice that 1 = HCF(3,1) = HCF(172,3) .
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 984, 705, 172?
Answer: HCF of 984, 705, 172 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 984, 705, 172 using Euclid's Algorithm?
Answer: For arbitrary numbers 984, 705, 172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.