Highest Common Factor of 376, 600, 16, 470 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 376, 600, 16, 470 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 376, 600, 16, 470 is 2 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 376, 600, 16, 470 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 376, 600, 16, 470 is 2.
HCF(376, 600, 16, 470) = 2
HCF of 376, 600, 16, 470 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 376, 600, 16, 470 is 2.
Highest Common Factor of 376,600,16,470 is 2
Step 1: Since 600 > 376, we apply the division lemma to 600 and 376, to get
600 = 376 x 1 + 224
Step 2: Since the reminder 376 ≠ 0, we apply division lemma to 224 and 376, to get
376 = 224 x 1 + 152
Step 3: We consider the new divisor 224 and the new remainder 152, and apply the division lemma to get
224 = 152 x 1 + 72
We consider the new divisor 152 and the new remainder 72,and apply the division lemma to get
152 = 72 x 2 + 8
We consider the new divisor 72 and the new remainder 8,and apply the division lemma to get
72 = 8 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 376 and 600 is 8
Notice that 8 = HCF(72,8) = HCF(152,72) = HCF(224,152) = HCF(376,224) = HCF(600,376) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 8, we apply the division lemma to 16 and 8, to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 8 and 16 is 8
Notice that 8 = HCF(16,8) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 470 > 8, we apply the division lemma to 470 and 8, to get
470 = 8 x 58 + 6
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 6 and 8, to get
8 = 6 x 1 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 470 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(470,8) .
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Frequently Asked Questions on HCF of 376, 600, 16, 470 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 376, 600, 16, 470?
Answer: HCF of 376, 600, 16, 470 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 376, 600, 16, 470 using Euclid's Algorithm?
Answer: For arbitrary numbers 376, 600, 16, 470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
