Highest Common Factor of 987, 277, 312, 242 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 987, 277, 312, 242 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 987, 277, 312, 242 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 987, 277, 312, 242 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 987, 277, 312, 242 is 1.
HCF(987, 277, 312, 242) = 1
HCF of 987, 277, 312, 242 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 987, 277, 312, 242 is 1.
Highest Common Factor of 987,277,312,242 is 1
Step 1: Since 987 > 277, we apply the division lemma to 987 and 277, to get
987 = 277 x 3 + 156
Step 2: Since the reminder 277 ≠ 0, we apply division lemma to 156 and 277, to get
277 = 156 x 1 + 121
Step 3: We consider the new divisor 156 and the new remainder 121, and apply the division lemma to get
156 = 121 x 1 + 35
We consider the new divisor 121 and the new remainder 35,and apply the division lemma to get
121 = 35 x 3 + 16
We consider the new divisor 35 and the new remainder 16,and apply the division lemma to get
35 = 16 x 2 + 3
We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get
16 = 3 x 5 + 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 987 and 277 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(35,16) = HCF(121,35) = HCF(156,121) = HCF(277,156) = HCF(987,277) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 312 > 1, we apply the division lemma to 312 and 1, to get
312 = 1 x 312 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 312 is 1
Notice that 1 = HCF(312,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 242 > 1, we apply the division lemma to 242 and 1, to get
242 = 1 x 242 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 242 is 1
Notice that 1 = HCF(242,1) .
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Frequently Asked Questions on HCF of 987, 277, 312, 242 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 987, 277, 312, 242?
Answer: HCF of 987, 277, 312, 242 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 987, 277, 312, 242 using Euclid's Algorithm?
Answer: For arbitrary numbers 987, 277, 312, 242 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.