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, 3318, 6496 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 172, 3318, 6496 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 172, 3318, 6496 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, 3318, 6496 is 2.
HCF(172, 3318, 6496) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 172, 3318, 6496 is 2.
Step 1: Since 3318 > 172, we apply the division lemma to 3318 and 172, to get
3318 = 172 x 19 + 50
Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 50 and 172, to get
172 = 50 x 3 + 22
Step 3: We consider the new divisor 50 and the new remainder 22, and apply the division lemma to get
50 = 22 x 2 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 172 and 3318 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(50,22) = HCF(172,50) = HCF(3318,172) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6496 > 2, we apply the division lemma to 6496 and 2, to get
6496 = 2 x 3248 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 6496 is 2
Notice that 2 = HCF(6496,2) .
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 172, 3318, 6496?
Answer: HCF of 172, 3318, 6496 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 172, 3318, 6496 using Euclid's Algorithm?
Answer: For arbitrary numbers 172, 3318, 6496 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.