Highest Common Factor of 770, 912, 300 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, 912, 300 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 770, 912, 300 is 2 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, 912, 300 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, 912, 300 is 2.
HCF(770, 912, 300) = 2
HCF of 770, 912, 300 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, 912, 300 is 2.
Highest Common Factor of 770,912,300 is 2
Step 1: Since 912 > 770, we apply the division lemma to 912 and 770, to get
912 = 770 x 1 + 142
Step 2: Since the reminder 770 ≠ 0, we apply division lemma to 142 and 770, to get
770 = 142 x 5 + 60
Step 3: We consider the new divisor 142 and the new remainder 60, and apply the division lemma to get
142 = 60 x 2 + 22
We consider the new divisor 60 and the new remainder 22,and apply the division lemma to get
60 = 22 x 2 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 770 and 912 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(60,22) = HCF(142,60) = HCF(770,142) = HCF(912,770) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 300 > 2, we apply the division lemma to 300 and 2, to get
300 = 2 x 150 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 300 is 2
Notice that 2 = HCF(300,2) .
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Frequently Asked Questions on HCF of 770, 912, 300 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, 912, 300?
Answer: HCF of 770, 912, 300 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 770, 912, 300 using Euclid's Algorithm?
Answer: For arbitrary numbers 770, 912, 300 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.