Highest Common Factor of 314, 972, 761 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 314, 972, 761 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 314, 972, 761 is 1 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 314, 972, 761 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 314, 972, 761 is 1.
HCF(314, 972, 761) = 1
HCF of 314, 972, 761 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 314, 972, 761 is 1.
Highest Common Factor of 314,972,761 is 1
Step 1: Since 972 > 314, we apply the division lemma to 972 and 314, to get
972 = 314 x 3 + 30
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 30 and 314, to get
314 = 30 x 10 + 14
Step 3: We consider the new divisor 30 and the new remainder 14, and apply the division lemma to get
30 = 14 x 2 + 2
We consider the new divisor 14 and the new remainder 2, and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 314 and 972 is 2
Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(314,30) = HCF(972,314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 761 > 2, we apply the division lemma to 761 and 2, to get
761 = 2 x 380 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 761 is 1
Notice that 1 = HCF(2,1) = HCF(761,2) .
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Frequently Asked Questions on HCF of 314, 972, 761 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 314, 972, 761?
Answer: HCF of 314, 972, 761 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 314, 972, 761 using Euclid's Algorithm?
Answer: For arbitrary numbers 314, 972, 761 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.