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 621, 78112 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 621, 78112 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 621, 78112 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 621, 78112 is 1.
HCF(621, 78112) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 621, 78112 is 1.
Step 1: Since 78112 > 621, we apply the division lemma to 78112 and 621, to get
78112 = 621 x 125 + 487
Step 2: Since the reminder 621 ≠ 0, we apply division lemma to 487 and 621, to get
621 = 487 x 1 + 134
Step 3: We consider the new divisor 487 and the new remainder 134, and apply the division lemma to get
487 = 134 x 3 + 85
We consider the new divisor 134 and the new remainder 85,and apply the division lemma to get
134 = 85 x 1 + 49
We consider the new divisor 85 and the new remainder 49,and apply the division lemma to get
85 = 49 x 1 + 36
We consider the new divisor 49 and the new remainder 36,and apply the division lemma to get
49 = 36 x 1 + 13
We consider the new divisor 36 and the new remainder 13,and apply the division lemma to get
36 = 13 x 2 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 621 and 78112 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(36,13) = HCF(49,36) = HCF(85,49) = HCF(134,85) = HCF(487,134) = HCF(621,487) = HCF(78112,621) .
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 621, 78112?
Answer: HCF of 621, 78112 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 621, 78112 using Euclid's Algorithm?
Answer: For arbitrary numbers 621, 78112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.