Highest Common Factor of 357, 974, 555 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 357, 974, 555 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 357, 974, 555 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 357, 974, 555 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 357, 974, 555 is 1.
HCF(357, 974, 555) = 1
HCF of 357, 974, 555 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 357, 974, 555 is 1.
Highest Common Factor of 357,974,555 is 1
Step 1: Since 974 > 357, we apply the division lemma to 974 and 357, to get
974 = 357 x 2 + 260
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 260 and 357, to get
357 = 260 x 1 + 97
Step 3: We consider the new divisor 260 and the new remainder 97, and apply the division lemma to get
260 = 97 x 2 + 66
We consider the new divisor 97 and the new remainder 66,and apply the division lemma to get
97 = 66 x 1 + 31
We consider the new divisor 66 and the new remainder 31,and apply the division lemma to get
66 = 31 x 2 + 4
We consider the new divisor 31 and the new remainder 4,and apply the division lemma to get
31 = 4 x 7 + 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 357 and 974 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(31,4) = HCF(66,31) = HCF(97,66) = HCF(260,97) = HCF(357,260) = HCF(974,357) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 555 > 1, we apply the division lemma to 555 and 1, to get
555 = 1 x 555 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 555 is 1
Notice that 1 = HCF(555,1) .
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Frequently Asked Questions on HCF of 357, 974, 555 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 357, 974, 555?
Answer: HCF of 357, 974, 555 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 357, 974, 555 using Euclid's Algorithm?
Answer: For arbitrary numbers 357, 974, 555 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.