Highest Common Factor of 900, 646, 774 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 900, 646, 774 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 900, 646, 774 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 900, 646, 774 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 900, 646, 774 is 2.
HCF(900, 646, 774) = 2
HCF of 900, 646, 774 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 900, 646, 774 is 2.
Highest Common Factor of 900,646,774 is 2
Step 1: Since 900 > 646, we apply the division lemma to 900 and 646, to get
900 = 646 x 1 + 254
Step 2: Since the reminder 646 ≠ 0, we apply division lemma to 254 and 646, to get
646 = 254 x 2 + 138
Step 3: We consider the new divisor 254 and the new remainder 138, and apply the division lemma to get
254 = 138 x 1 + 116
We consider the new divisor 138 and the new remainder 116,and apply the division lemma to get
138 = 116 x 1 + 22
We consider the new divisor 116 and the new remainder 22,and apply the division lemma to get
116 = 22 x 5 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 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 900 and 646 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(116,22) = HCF(138,116) = HCF(254,138) = HCF(646,254) = HCF(900,646) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 774 > 2, we apply the division lemma to 774 and 2, to get
774 = 2 x 387 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 774 is 2
Notice that 2 = HCF(774,2) .
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Frequently Asked Questions on HCF of 900, 646, 774 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 900, 646, 774?
Answer: HCF of 900, 646, 774 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 900, 646, 774 using Euclid's Algorithm?
Answer: For arbitrary numbers 900, 646, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.