Highest Common Factor of 91, 56, 749 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 91, 56, 749 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 91, 56, 749 is 7 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 91, 56, 749 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 91, 56, 749 is 7.
HCF(91, 56, 749) = 7
HCF of 91, 56, 749 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 91, 56, 749 is 7.
Highest Common Factor of 91,56,749 is 7
Step 1: Since 91 > 56, we apply the division lemma to 91 and 56, to get
91 = 56 x 1 + 35
Step 2: Since the reminder 56 ≠ 0, we apply division lemma to 35 and 56, to get
56 = 35 x 1 + 21
Step 3: We consider the new divisor 35 and the new remainder 21, and apply the division lemma to get
35 = 21 x 1 + 14
We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 91 and 56 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(35,21) = HCF(56,35) = HCF(91,56) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 749 > 7, we apply the division lemma to 749 and 7, to get
749 = 7 x 107 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 749 is 7
Notice that 7 = HCF(749,7) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 91, 56, 749 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 91, 56, 749?
Answer: HCF of 91, 56, 749 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 91, 56, 749 using Euclid's Algorithm?
Answer: For arbitrary numbers 91, 56, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.