Highest Common Factor of 536, 735 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 536, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 536, 735 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 536, 735 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 536, 735 is 1.
HCF(536, 735) = 1
HCF of 536, 735 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 536, 735 is 1.
Highest Common Factor of 536,735 is 1
Step 1: Since 735 > 536, we apply the division lemma to 735 and 536, to get
735 = 536 x 1 + 199
Step 2: Since the reminder 536 ≠ 0, we apply division lemma to 199 and 536, to get
536 = 199 x 2 + 138
Step 3: We consider the new divisor 199 and the new remainder 138, and apply the division lemma to get
199 = 138 x 1 + 61
We consider the new divisor 138 and the new remainder 61,and apply the division lemma to get
138 = 61 x 2 + 16
We consider the new divisor 61 and the new remainder 16,and apply the division lemma to get
61 = 16 x 3 + 13
We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get
16 = 13 x 1 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 536 and 735 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(61,16) = HCF(138,61) = HCF(199,138) = HCF(536,199) = HCF(735,536) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 536, 735 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 536, 735?
Answer: HCF of 536, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 536, 735 using Euclid's Algorithm?
Answer: For arbitrary numbers 536, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.