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 516, 852, 174 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 852, 174 is 6 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 516, 852, 174 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 516, 852, 174 is 6.
HCF(516, 852, 174) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 516, 852, 174 is 6.
Step 1: Since 852 > 516, we apply the division lemma to 852 and 516, to get
852 = 516 x 1 + 336
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 336 and 516, to get
516 = 336 x 1 + 180
Step 3: We consider the new divisor 336 and the new remainder 180, and apply the division lemma to get
336 = 180 x 1 + 156
We consider the new divisor 180 and the new remainder 156,and apply the division lemma to get
180 = 156 x 1 + 24
We consider the new divisor 156 and the new remainder 24,and apply the division lemma to get
156 = 24 x 6 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 516 and 852 is 12
Notice that 12 = HCF(24,12) = HCF(156,24) = HCF(180,156) = HCF(336,180) = HCF(516,336) = HCF(852,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 174 > 12, we apply the division lemma to 174 and 12, to get
174 = 12 x 14 + 6
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 6 and 12, to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 12 and 174 is 6
Notice that 6 = HCF(12,6) = HCF(174,12) .
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 516, 852, 174?
Answer: HCF of 516, 852, 174 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 852, 174 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 852, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.