Highest Common Factor of 977, 132, 298 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 977, 132, 298 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 977, 132, 298 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 977, 132, 298 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 977, 132, 298 is 1.
HCF(977, 132, 298) = 1
HCF of 977, 132, 298 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 977, 132, 298 is 1.
Highest Common Factor of 977,132,298 is 1
Step 1: Since 977 > 132, we apply the division lemma to 977 and 132, to get
977 = 132 x 7 + 53
Step 2: Since the reminder 132 ≠ 0, we apply division lemma to 53 and 132, to get
132 = 53 x 2 + 26
Step 3: We consider the new divisor 53 and the new remainder 26, and apply the division lemma to get
53 = 26 x 2 + 1
We consider the new divisor 26 and the new remainder 1, and apply the division lemma to get
26 = 1 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 977 and 132 is 1
Notice that 1 = HCF(26,1) = HCF(53,26) = HCF(132,53) = HCF(977,132) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 298 > 1, we apply the division lemma to 298 and 1, to get
298 = 1 x 298 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 298 is 1
Notice that 1 = HCF(298,1) .
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Frequently Asked Questions on HCF of 977, 132, 298 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 977, 132, 298?
Answer: HCF of 977, 132, 298 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 977, 132, 298 using Euclid's Algorithm?
Answer: For arbitrary numbers 977, 132, 298 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
