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 268, 465, 535, 524 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 268, 465, 535, 524 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 268, 465, 535, 524 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 268, 465, 535, 524 is 1.
HCF(268, 465, 535, 524) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 268, 465, 535, 524 is 1.
Step 1: Since 465 > 268, we apply the division lemma to 465 and 268, to get
465 = 268 x 1 + 197
Step 2: Since the reminder 268 ≠ 0, we apply division lemma to 197 and 268, to get
268 = 197 x 1 + 71
Step 3: We consider the new divisor 197 and the new remainder 71, and apply the division lemma to get
197 = 71 x 2 + 55
We consider the new divisor 71 and the new remainder 55,and apply the division lemma to get
71 = 55 x 1 + 16
We consider the new divisor 55 and the new remainder 16,and apply the division lemma to get
55 = 16 x 3 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 268 and 465 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(55,16) = HCF(71,55) = HCF(197,71) = HCF(268,197) = HCF(465,268) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 535 > 1, we apply the division lemma to 535 and 1, to get
535 = 1 x 535 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 535 is 1
Notice that 1 = HCF(535,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 524 > 1, we apply the division lemma to 524 and 1, to get
524 = 1 x 524 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 524 is 1
Notice that 1 = HCF(524,1) .
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 268, 465, 535, 524?
Answer: HCF of 268, 465, 535, 524 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 268, 465, 535, 524 using Euclid's Algorithm?
Answer: For arbitrary numbers 268, 465, 535, 524 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.