Highest Common Factor of 977, 298, 278, 285 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, 298, 278, 285 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 977, 298, 278, 285 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, 298, 278, 285 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, 298, 278, 285 is 1.
HCF(977, 298, 278, 285) = 1
HCF of 977, 298, 278, 285 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, 298, 278, 285 is 1.
Highest Common Factor of 977,298,278,285 is 1
Step 1: Since 977 > 298, we apply the division lemma to 977 and 298, to get
977 = 298 x 3 + 83
Step 2: Since the reminder 298 ≠ 0, we apply division lemma to 83 and 298, to get
298 = 83 x 3 + 49
Step 3: We consider the new divisor 83 and the new remainder 49, and apply the division lemma to get
83 = 49 x 1 + 34
We consider the new divisor 49 and the new remainder 34,and apply the division lemma to get
49 = 34 x 1 + 15
We consider the new divisor 34 and the new remainder 15,and apply the division lemma to get
34 = 15 x 2 + 4
We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get
15 = 4 x 3 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 977 and 298 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(34,15) = HCF(49,34) = HCF(83,49) = HCF(298,83) = HCF(977,298) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 278 > 1, we apply the division lemma to 278 and 1, to get
278 = 1 x 278 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 278 is 1
Notice that 1 = HCF(278,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 285 > 1, we apply the division lemma to 285 and 1, to get
285 = 1 x 285 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 285 is 1
Notice that 1 = HCF(285,1) .
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Frequently Asked Questions on HCF of 977, 298, 278, 285 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, 298, 278, 285?
Answer: HCF of 977, 298, 278, 285 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 977, 298, 278, 285 using Euclid's Algorithm?
Answer: For arbitrary numbers 977, 298, 278, 285 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.