Highest Common Factor of 972, 6910, 6578 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 972, 6910, 6578 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 6910, 6578 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 972, 6910, 6578 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 972, 6910, 6578 is 2.
HCF(972, 6910, 6578) = 2
HCF of 972, 6910, 6578 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 6910, 6578 is 2.
Highest Common Factor of 972,6910,6578 is 2
Step 1: Since 6910 > 972, we apply the division lemma to 6910 and 972, to get
6910 = 972 x 7 + 106
Step 2: Since the reminder 972 ≠ 0, we apply division lemma to 106 and 972, to get
972 = 106 x 9 + 18
Step 3: We consider the new divisor 106 and the new remainder 18, and apply the division lemma to get
106 = 18 x 5 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 972 and 6910 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(106,18) = HCF(972,106) = HCF(6910,972) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6578 > 2, we apply the division lemma to 6578 and 2, to get
6578 = 2 x 3289 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 6578 is 2
Notice that 2 = HCF(6578,2) .
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Frequently Asked Questions on HCF of 972, 6910, 6578 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 972, 6910, 6578?
Answer: HCF of 972, 6910, 6578 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 6910, 6578 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 6910, 6578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.