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 505, 637, 501 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 505, 637, 501 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 505, 637, 501 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 505, 637, 501 is 1.
HCF(505, 637, 501) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 505, 637, 501 is 1.
Step 1: Since 637 > 505, we apply the division lemma to 637 and 505, to get
637 = 505 x 1 + 132
Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 132 and 505, to get
505 = 132 x 3 + 109
Step 3: We consider the new divisor 132 and the new remainder 109, and apply the division lemma to get
132 = 109 x 1 + 23
We consider the new divisor 109 and the new remainder 23,and apply the division lemma to get
109 = 23 x 4 + 17
We consider the new divisor 23 and the new remainder 17,and apply the division lemma to get
23 = 17 x 1 + 6
We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get
17 = 6 x 2 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 505 and 637 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(23,17) = HCF(109,23) = HCF(132,109) = HCF(505,132) = HCF(637,505) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 501 > 1, we apply the division lemma to 501 and 1, to get
501 = 1 x 501 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 501 is 1
Notice that 1 = HCF(501,1) .
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 505, 637, 501?
Answer: HCF of 505, 637, 501 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 505, 637, 501 using Euclid's Algorithm?
Answer: For arbitrary numbers 505, 637, 501 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.