Highest Common Factor of 77, 286, 748 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 77, 286, 748 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 77, 286, 748 is 11 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 77, 286, 748 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 77, 286, 748 is 11.
HCF(77, 286, 748) = 11
HCF of 77, 286, 748 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 77, 286, 748 is 11.
Highest Common Factor of 77,286,748 is 11
Step 1: Since 286 > 77, we apply the division lemma to 286 and 77, to get
286 = 77 x 3 + 55
Step 2: Since the reminder 77 ≠ 0, we apply division lemma to 55 and 77, to get
77 = 55 x 1 + 22
Step 3: We consider the new divisor 55 and the new remainder 22, and apply the division lemma to get
55 = 22 x 2 + 11
We consider the new divisor 22 and the new remainder 11, and apply the division lemma to get
22 = 11 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 77 and 286 is 11
Notice that 11 = HCF(22,11) = HCF(55,22) = HCF(77,55) = HCF(286,77) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 748 > 11, we apply the division lemma to 748 and 11, to get
748 = 11 x 68 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 11 and 748 is 11
Notice that 11 = HCF(748,11) .
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Frequently Asked Questions on HCF of 77, 286, 748 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 77, 286, 748?
Answer: HCF of 77, 286, 748 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 77, 286, 748 using Euclid's Algorithm?
Answer: For arbitrary numbers 77, 286, 748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.