Highest Common Factor of 420, 598, 915 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 420, 598, 915 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 598, 915 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 420, 598, 915 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 420, 598, 915 is 1.
HCF(420, 598, 915) = 1
HCF of 420, 598, 915 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 598, 915 is 1.
Highest Common Factor of 420,598,915 is 1
Step 1: Since 598 > 420, we apply the division lemma to 598 and 420, to get
598 = 420 x 1 + 178
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 178 and 420, to get
420 = 178 x 2 + 64
Step 3: We consider the new divisor 178 and the new remainder 64, and apply the division lemma to get
178 = 64 x 2 + 50
We consider the new divisor 64 and the new remainder 50,and apply the division lemma to get
64 = 50 x 1 + 14
We consider the new divisor 50 and the new remainder 14,and apply the division lemma to get
50 = 14 x 3 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 420 and 598 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(50,14) = HCF(64,50) = HCF(178,64) = HCF(420,178) = HCF(598,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 915 > 2, we apply the division lemma to 915 and 2, to get
915 = 2 x 457 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 915 is 1
Notice that 1 = HCF(2,1) = HCF(915,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 420, 598, 915 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 420, 598, 915?
Answer: HCF of 420, 598, 915 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 598, 915 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 598, 915 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.