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 598, 686, 507, 40 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 598, 686, 507, 40 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 598, 686, 507, 40 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 598, 686, 507, 40 is 1.
HCF(598, 686, 507, 40) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 598, 686, 507, 40 is 1.
Step 1: Since 686 > 598, we apply the division lemma to 686 and 598, to get
686 = 598 x 1 + 88
Step 2: Since the reminder 598 ≠ 0, we apply division lemma to 88 and 598, to get
598 = 88 x 6 + 70
Step 3: We consider the new divisor 88 and the new remainder 70, and apply the division lemma to get
88 = 70 x 1 + 18
We consider the new divisor 70 and the new remainder 18,and apply the division lemma to get
70 = 18 x 3 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 598 and 686 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(70,18) = HCF(88,70) = HCF(598,88) = HCF(686,598) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 507 > 2, we apply the division lemma to 507 and 2, to get
507 = 2 x 253 + 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 507 is 1
Notice that 1 = HCF(2,1) = HCF(507,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 40 > 1, we apply the division lemma to 40 and 1, to get
40 = 1 x 40 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 40 is 1
Notice that 1 = HCF(40,1) .
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 598, 686, 507, 40?
Answer: HCF of 598, 686, 507, 40 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 598, 686, 507, 40 using Euclid's Algorithm?
Answer: For arbitrary numbers 598, 686, 507, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.