Highest Common Factor of 770, 896, 49 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 770, 896, 49 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 770, 896, 49 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 770, 896, 49 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 770, 896, 49 is 7.
HCF(770, 896, 49) = 7
HCF of 770, 896, 49 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 770, 896, 49 is 7.
Highest Common Factor of 770,896,49 is 7
Step 1: Since 896 > 770, we apply the division lemma to 896 and 770, to get
896 = 770 x 1 + 126
Step 2: Since the reminder 770 ≠ 0, we apply division lemma to 126 and 770, to get
770 = 126 x 6 + 14
Step 3: We consider the new divisor 126 and the new remainder 14, and apply the division lemma to get
126 = 14 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 770 and 896 is 14
Notice that 14 = HCF(126,14) = HCF(770,126) = HCF(896,770) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 49 > 14, we apply the division lemma to 49 and 14, to get
49 = 14 x 3 + 7
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 7 and 14, 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 14 and 49 is 7
Notice that 7 = HCF(14,7) = HCF(49,14) .
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Frequently Asked Questions on HCF of 770, 896, 49 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 770, 896, 49?
Answer: HCF of 770, 896, 49 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 770, 896, 49 using Euclid's Algorithm?
Answer: For arbitrary numbers 770, 896, 49 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.