Highest Common Factor of 407, 700 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 407, 700 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 407, 700 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 407, 700 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 407, 700 is 1.
HCF(407, 700) = 1
HCF of 407, 700 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 407, 700 is 1.
Highest Common Factor of 407,700 is 1
Step 1: Since 700 > 407, we apply the division lemma to 700 and 407, to get
700 = 407 x 1 + 293
Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 293 and 407, to get
407 = 293 x 1 + 114
Step 3: We consider the new divisor 293 and the new remainder 114, and apply the division lemma to get
293 = 114 x 2 + 65
We consider the new divisor 114 and the new remainder 65,and apply the division lemma to get
114 = 65 x 1 + 49
We consider the new divisor 65 and the new remainder 49,and apply the division lemma to get
65 = 49 x 1 + 16
We consider the new divisor 49 and the new remainder 16,and apply the division lemma to get
49 = 16 x 3 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 407 and 700 is 1
Notice that 1 = HCF(16,1) = HCF(49,16) = HCF(65,49) = HCF(114,65) = HCF(293,114) = HCF(407,293) = HCF(700,407) .
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Frequently Asked Questions on HCF of 407, 700 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 407, 700?
Answer: HCF of 407, 700 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 407, 700 using Euclid's Algorithm?
Answer: For arbitrary numbers 407, 700 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.