Highest Common Factor of 749, 903, 686 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 749, 903, 686 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 749, 903, 686 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 749, 903, 686 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 749, 903, 686 is 7.
HCF(749, 903, 686) = 7
HCF of 749, 903, 686 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 749, 903, 686 is 7.
Highest Common Factor of 749,903,686 is 7
Step 1: Since 903 > 749, we apply the division lemma to 903 and 749, to get
903 = 749 x 1 + 154
Step 2: Since the reminder 749 ≠ 0, we apply division lemma to 154 and 749, to get
749 = 154 x 4 + 133
Step 3: We consider the new divisor 154 and the new remainder 133, and apply the division lemma to get
154 = 133 x 1 + 21
We consider the new divisor 133 and the new remainder 21,and apply the division lemma to get
133 = 21 x 6 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 749 and 903 is 7
Notice that 7 = HCF(21,7) = HCF(133,21) = HCF(154,133) = HCF(749,154) = HCF(903,749) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 686 > 7, we apply the division lemma to 686 and 7, to get
686 = 7 x 98 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 686 is 7
Notice that 7 = HCF(686,7) .
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Frequently Asked Questions on HCF of 749, 903, 686 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 749, 903, 686?
Answer: HCF of 749, 903, 686 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 749, 903, 686 using Euclid's Algorithm?
Answer: For arbitrary numbers 749, 903, 686 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.