Highest Common Factor of 98, 357, 186, 302 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 98, 357, 186, 302 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 98, 357, 186, 302 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 98, 357, 186, 302 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 98, 357, 186, 302 is 1.
HCF(98, 357, 186, 302) = 1
HCF of 98, 357, 186, 302 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 98, 357, 186, 302 is 1.
Highest Common Factor of 98,357,186,302 is 1
Step 1: Since 357 > 98, we apply the division lemma to 357 and 98, to get
357 = 98 x 3 + 63
Step 2: Since the reminder 98 ≠ 0, we apply division lemma to 63 and 98, to get
98 = 63 x 1 + 35
Step 3: We consider the new divisor 63 and the new remainder 35, and apply the division lemma to get
63 = 35 x 1 + 28
We consider the new divisor 35 and the new remainder 28,and apply the division lemma to get
35 = 28 x 1 + 7
We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 98 and 357 is 7
Notice that 7 = HCF(28,7) = HCF(35,28) = HCF(63,35) = HCF(98,63) = HCF(357,98) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 186 > 7, we apply the division lemma to 186 and 7, to get
186 = 7 x 26 + 4
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get
7 = 4 x 1 + 3
Step 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 7 and 186 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(186,7) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 302 > 1, we apply the division lemma to 302 and 1, to get
302 = 1 x 302 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 302 is 1
Notice that 1 = HCF(302,1) .
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Frequently Asked Questions on HCF of 98, 357, 186, 302 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 98, 357, 186, 302?
Answer: HCF of 98, 357, 186, 302 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 98, 357, 186, 302 using Euclid's Algorithm?
Answer: For arbitrary numbers 98, 357, 186, 302 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.