Highest Common Factor of 975, 728, 842 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 975, 728, 842 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 975, 728, 842 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 975, 728, 842 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 975, 728, 842 is 1.
HCF(975, 728, 842) = 1
HCF of 975, 728, 842 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 975, 728, 842 is 1.
Highest Common Factor of 975,728,842 is 1
Step 1: Since 975 > 728, we apply the division lemma to 975 and 728, to get
975 = 728 x 1 + 247
Step 2: Since the reminder 728 ≠ 0, we apply division lemma to 247 and 728, to get
728 = 247 x 2 + 234
Step 3: We consider the new divisor 247 and the new remainder 234, and apply the division lemma to get
247 = 234 x 1 + 13
We consider the new divisor 234 and the new remainder 13, and apply the division lemma to get
234 = 13 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 975 and 728 is 13
Notice that 13 = HCF(234,13) = HCF(247,234) = HCF(728,247) = HCF(975,728) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 842 > 13, we apply the division lemma to 842 and 13, to get
842 = 13 x 64 + 10
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 10 and 13, to get
13 = 10 x 1 + 3
Step 3: We consider the new divisor 10 and the new remainder 3, and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 842 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(842,13) .
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Frequently Asked Questions on HCF of 975, 728, 842 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 975, 728, 842?
Answer: HCF of 975, 728, 842 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 975, 728, 842 using Euclid's Algorithm?
Answer: For arbitrary numbers 975, 728, 842 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.