Highest Common Factor of 754, 735, 111 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 754, 735, 111 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 754, 735, 111 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 754, 735, 111 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 754, 735, 111 is 1.
HCF(754, 735, 111) = 1
HCF of 754, 735, 111 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 754, 735, 111 is 1.
Highest Common Factor of 754,735,111 is 1
Step 1: Since 754 > 735, we apply the division lemma to 754 and 735, to get
754 = 735 x 1 + 19
Step 2: Since the reminder 735 ≠ 0, we apply division lemma to 19 and 735, to get
735 = 19 x 38 + 13
Step 3: We consider the new divisor 19 and the new remainder 13, and apply the division lemma to get
19 = 13 x 1 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 754 and 735 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(735,19) = HCF(754,735) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 111 > 1, we apply the division lemma to 111 and 1, to get
111 = 1 x 111 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 111 is 1
Notice that 1 = HCF(111,1) .
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Frequently Asked Questions on HCF of 754, 735, 111 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 754, 735, 111?
Answer: HCF of 754, 735, 111 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 754, 735, 111 using Euclid's Algorithm?
Answer: For arbitrary numbers 754, 735, 111 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.