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 504, 902, 617, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 902, 617, 21 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 504, 902, 617, 21 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 504, 902, 617, 21 is 1.
HCF(504, 902, 617, 21) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 504, 902, 617, 21 is 1.
Step 1: Since 902 > 504, we apply the division lemma to 902 and 504, to get
902 = 504 x 1 + 398
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 398 and 504, to get
504 = 398 x 1 + 106
Step 3: We consider the new divisor 398 and the new remainder 106, and apply the division lemma to get
398 = 106 x 3 + 80
We consider the new divisor 106 and the new remainder 80,and apply the division lemma to get
106 = 80 x 1 + 26
We consider the new divisor 80 and the new remainder 26,and apply the division lemma to get
80 = 26 x 3 + 2
We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 504 and 902 is 2
Notice that 2 = HCF(26,2) = HCF(80,26) = HCF(106,80) = HCF(398,106) = HCF(504,398) = HCF(902,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 617 > 2, we apply the division lemma to 617 and 2, to get
617 = 2 x 308 + 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 617 is 1
Notice that 1 = HCF(2,1) = HCF(617,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21 is 1
Notice that 1 = HCF(21,1) .
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 504, 902, 617, 21?
Answer: HCF of 504, 902, 617, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 902, 617, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 902, 617, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.