Highest Common Factor of 357, 907, 416 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, 907, 416 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 357, 907, 416 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, 907, 416 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, 907, 416 is 1.
HCF(357, 907, 416) = 1
HCF of 357, 907, 416 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, 907, 416 is 1.
Highest Common Factor of 357,907,416 is 1
Step 1: Since 907 > 357, we apply the division lemma to 907 and 357, to get
907 = 357 x 2 + 193
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 193 and 357, to get
357 = 193 x 1 + 164
Step 3: We consider the new divisor 193 and the new remainder 164, and apply the division lemma to get
193 = 164 x 1 + 29
We consider the new divisor 164 and the new remainder 29,and apply the division lemma to get
164 = 29 x 5 + 19
We consider the new divisor 29 and the new remainder 19,and apply the division lemma to get
29 = 19 x 1 + 10
We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get
19 = 10 x 1 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 357 and 907 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(29,19) = HCF(164,29) = HCF(193,164) = HCF(357,193) = HCF(907,357) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 416 > 1, we apply the division lemma to 416 and 1, to get
416 = 1 x 416 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 416 is 1
Notice that 1 = HCF(416,1) .
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Frequently Asked Questions on HCF of 357, 907, 416 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, 907, 416?
Answer: HCF of 357, 907, 416 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 357, 907, 416 using Euclid's Algorithm?
Answer: For arbitrary numbers 357, 907, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
